/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 202 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 6 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(16) CdtProblem
    (17) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CdtProblem
    (19) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CdtProblem
    (21) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CdtProblem
    (23) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (24) CdtProblem
    (25) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CdtProblem
    (27) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (28) CdtProblem
    (29) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (32) CdtProblem
    (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
    (40) CdtProblem
    (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms]
    (44) CdtProblem
    (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 45 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
    (52) CdtProblem
    (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms]
    (68) CdtProblem
    (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms]
    (72) CdtProblem
    (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (80) CdtProblem
    (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms]
    (84) CdtProblem
    (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms]
    (92) CdtProblem
    (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms]
    (112) CdtProblem
    (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms]
    (116) CdtProblem
    (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms]
    (120) CdtProblem
    (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (124) CdtProblem
    (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (128) CdtProblem
    (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
    (140) CdtProblem
    (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
    (144) CdtProblem
    (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms]
    (148) CdtProblem
    (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
(151) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(152) CpxRelTRS
    (153) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CpxWeightedTrs
    (155) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CpxTypedWeightedTrs
    (157) CompletionProof [UPPER BOUND(ID), 0 ms]
    (158) CpxTypedWeightedCompleteTrs
        (159) NarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
        (160) CpxTypedWeightedCompleteTrs
        (161) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 20 ms]
        (162) CpxRNTS
        (163) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CpxRNTS
    (165) CompletionProof [UPPER BOUND(ID), 0 ms]
    (166) CpxTypedWeightedCompleteTrs
        (167) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
        (168) CpxRNTS


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

(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(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y
   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(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   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(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y
   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(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   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(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y
   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(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(app(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y
   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(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(8)
Obligation:
Innermost TRS:
Rules:
app(app(\, x), x) -> e
app(app(\, e), x) -> x
app(app(\, x), app(app(., x), y)) -> y
app(app(\, app(app(/, x), y)), x) -> y
app(app(/, x), x) -> e
app(app(/, x), e) -> x
app(app(/, app(app(., y), x)), x) -> y
app(app(/, x), app(app(\, y), x)) -> y
app(app(., e), x) -> x
app(app(., x), e) -> x
app(app(., x), app(app(\, x), y)) -> y
app(app(., app(app(/, y), x)), x) -> y
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(\) -> \
encArg(e) -> e
encArg(.) -> .
encArg(/) -> /
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_\ -> \
encode_e -> e
encode_. -> .
encode_/ -> /
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2
encode_true -> true
encode_false -> false

Types:
app :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
\ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
e :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
. :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
/ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
map :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
nil :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
cons :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
filter :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
true :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
false :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_\ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_e :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_. :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_/ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
hole_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app1_0 :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
gen_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app2_0 :: Nat -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app

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

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

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

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

(10)
Obligation:
Innermost TRS:
Rules:
app(app(\, x), x) -> e
app(app(\, e), x) -> x
app(app(\, x), app(app(., x), y)) -> y
app(app(\, app(app(/, x), y)), x) -> y
app(app(/, x), x) -> e
app(app(/, x), e) -> x
app(app(/, app(app(., y), x)), x) -> y
app(app(/, x), app(app(\, y), x)) -> y
app(app(., e), x) -> x
app(app(., x), e) -> x
app(app(., x), app(app(\, x), y)) -> y
app(app(., app(app(/, y), x)), x) -> y
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(\) -> \
encArg(e) -> e
encArg(.) -> .
encArg(/) -> /
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_\ -> \
encode_e -> e
encode_. -> .
encode_/ -> /
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2
encode_true -> true
encode_false -> false

Types:
app :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
\ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
e :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
. :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
/ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
map :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
nil :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
cons :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
filter :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
true :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
false :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_\ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_e :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_. :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_/ :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
hole_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app1_0 :: \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app
gen_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app2_0 :: Nat -> \:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app


Generator Equations:
gen_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app2_0(0) <=> \
gen_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app2_0(+(x, 1)) <=> cons_app(\, gen_\:e:.:/:map:nil:cons:filter:filter2:true:false:cons_app2_0(x))


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

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

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

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

(12)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   app(app(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y
   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(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

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


The TRS R consists of the following rules:

   app(app(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y
   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(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(16)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\) -> c
   ENCARG(e) -> c1
   ENCARG(.) -> c2
   ENCARG(/) -> c3
   ENCARG(map) -> c4
   ENCARG(nil) -> c5
   ENCARG(cons) -> c6
   ENCARG(filter) -> c7
   ENCARG(filter2) -> c8
   ENCARG(true) -> c9
   ENCARG(false) -> c10
   ENCARG(cons_app(z0, z1)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_\ -> c13
   ENCODE_E -> c14
   ENCODE_. -> c15
   ENCODE_/ -> c16
   ENCODE_MAP -> c17
   ENCODE_NIL -> c18
   ENCODE_CONS -> c19
   ENCODE_FILTER -> c20
   ENCODE_FILTER2 -> c21
   ENCODE_TRUE -> c22
   ENCODE_FALSE -> c23
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(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) -> c38
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(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) -> c40(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) -> c41(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(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) -> c38
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(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) -> c40(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) -> c41(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_\, encode_e, encode_., encode_/, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_\, ENCODE_E, ENCODE_., ENCODE_/, 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_3, c12_3, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37_5, c38, c39_5, c40_4, c41_2


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

(17) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 22 trailing nodes:
   ENCODE_FALSE -> c23
   ENCODE_CONS -> c19
   ENCODE_. -> c15
   ENCODE_E -> c14
   ENCARG(nil) -> c5
   ENCODE_FILTER -> c20
   ENCARG(/) -> c3
   ENCARG(filter2) -> c8
   ENCODE_NIL -> c18
   ENCARG(true) -> c9
   ENCODE_MAP -> c17
   ENCARG(e) -> c1
   ENCODE_FILTER2 -> c21
   ENCARG(map) -> c4
   ENCARG(false) -> c10
   ENCARG(.) -> c2
   ENCARG(cons) -> c6
   ENCARG(filter) -> c7
   ENCODE_/ -> c16
   ENCODE_\ -> c13
   ENCARG(\) -> c
   ENCODE_TRUE -> c22

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

(18)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(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) -> c38
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(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) -> c40(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) -> c41(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(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) -> c38
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(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) -> c40(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) -> c41(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_\, encode_e, encode_., encode_/, 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:   c11_3, c12_3, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37_5, c38, c39_5, c40_4, c41_2


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

(19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing tuple parts
----------------------------------------

(20)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_\, encode_e, encode_., encode_/, 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:   c11_3, c12_3, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c39_2, c40_1, c41_1


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

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

(22)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_\, encode_e, encode_., encode_/, 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:   c11_3, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c39_2, c40_1, c41_1, c_1


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

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

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

(24)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_\, encode_e, encode_., encode_/, 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:   c11_3, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c39_2, c40_1, c41_1, c_1


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

(25) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(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:   c11_3, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c39_2, c40_1, c41_1, c_1


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

(27) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0), ENCARG(\))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0), ENCARG(e))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0), ENCARG(.))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0), ENCARG(/))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(\, x1)) -> c11(APP(\, encArg(x1)), ENCARG(\), ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(APP(e, encArg(x1)), ENCARG(e), ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(APP(., encArg(x1)), ENCARG(.), ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(APP(/, encArg(x1)), ENCARG(/), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0), ENCARG(\))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0), ENCARG(e))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0), ENCARG(.))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0), ENCARG(/))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(\, x1)) -> c11(APP(\, encArg(x1)), ENCARG(\), ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(APP(e, encArg(x1)), ENCARG(e), ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(APP(., encArg(x1)), ENCARG(.), ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(APP(/, encArg(x1)), ENCARG(/), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c39_2, c40_1, c41_1, c_1, c11_3


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

(29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 33 trailing tuple parts
----------------------------------------

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c39_2, c40_1, c41_1, c_1, c11_3, c11_2, c11_1


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

(31) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c39(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by 
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, e), app(\, z0)), z0), x2), APP(app(\, z0), z0))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, e), app(/, z0)), z0), x2), APP(app(/, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(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)) -> c39(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)) -> c39(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))

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, e), app(\, z0)), z0), x2), APP(app(\, z0), z0))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, e), app(/, z0)), z0), x2), APP(app(/, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(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)) -> c39(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)) -> c39(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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, e), app(\, z0)), z0), x2), APP(app(\, z0), z0))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, e), app(/, z0)), z0), x2), APP(app(/, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(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)) -> c39(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)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c_1, c11_3, c11_2, c11_1, c39_2


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

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c_1, c11_3, c11_2, c11_1, c39_2, c39_1


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

(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   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(\, x1) -> c(APP(\, encArg(x1)))
   ENCODE_APP(e, x1) -> c(APP(e, encArg(x1)))
   ENCODE_APP(., x1) -> c(APP(., encArg(x1)))
   ENCODE_APP(/, x1) -> c(APP(/, 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)))

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   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(\, x1) -> c(APP(\, encArg(x1)))
   ENCODE_APP(e, x1) -> c(APP(e, encArg(x1)))
   ENCODE_APP(., x1) -> c(APP(., encArg(x1)))
   ENCODE_APP(/, x1) -> c(APP(/, 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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_3, c11_2, c11_1, c39_2, c39_1, c_1


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

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(e, x1) -> c(APP(e, encArg(x1)))
   ENCODE_APP(\, x1) -> c(APP(\, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(/, x1) -> c(APP(/, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(., x1) -> c(APP(., encArg(x1)))

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_3, c11_2, c11_1, c39_2, c39_1, c_1


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

(39) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c11(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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(x1, x2))) -> c11(APP(\, app(encArg(x1), encArg(x2))), ENCARG(\), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(APP(e, app(encArg(x1), encArg(x2))), ENCARG(e), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(APP(., app(encArg(x1), encArg(x2))), ENCARG(.), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(APP(/, app(encArg(x1), encArg(x2))), ENCARG(/), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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(x1, x2))) -> c11(APP(\, app(encArg(x1), encArg(x2))), ENCARG(\), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(APP(e, app(encArg(x1), encArg(x2))), ENCARG(e), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(APP(., app(encArg(x1), encArg(x2))), ENCARG(.), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(APP(/, app(encArg(x1), encArg(x2))), ENCARG(/), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(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))) -> c11(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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_3, c11_2, c11_1, c39_2, c39_1, c_1


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

(41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 22 trailing tuple parts
----------------------------------------

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_3, c11_2, c11_1, c39_2, c39_1, c_1


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

(43) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c11(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)), ENCARG(\))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)), ENCARG(e))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)), ENCARG(.))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)), ENCARG(/))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(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))) -> c11(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, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(APP(app(e, encArg(x1)), encArg(x2)), ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(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)) -> c11(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)), ENCARG(\))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)), ENCARG(e))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)), ENCARG(.))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)), ENCARG(/))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(APP(app(e, encArg(x1)), encArg(x2)), ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(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)) -> c11(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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing tuple parts
----------------------------------------

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, \)) -> c11(APP(encArg(x0), \), ENCARG(x0)) by 
   ENCARG(cons_app(\, \)) -> c11(APP(\, \), ENCARG(\))
   ENCARG(cons_app(e, \)) -> c11(APP(e, \), ENCARG(e))
   ENCARG(cons_app(., \)) -> c11(APP(., \), ENCARG(.))
   ENCARG(cons_app(/, \)) -> c11(APP(/, \), ENCARG(/))
   ENCARG(cons_app(map, \)) -> c11(APP(map, \), ENCARG(map))
   ENCARG(cons_app(nil, \)) -> c11(APP(nil, \), ENCARG(nil))
   ENCARG(cons_app(cons, \)) -> c11(APP(cons, \), ENCARG(cons))
   ENCARG(cons_app(filter, \)) -> c11(APP(filter, \), ENCARG(filter))
   ENCARG(cons_app(filter2, \)) -> c11(APP(filter2, \), ENCARG(filter2))
   ENCARG(cons_app(true, \)) -> c11(APP(true, \), ENCARG(true))
   ENCARG(cons_app(false, \)) -> c11(APP(false, \), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), \)) -> c11(APP(app(encArg(z0), encArg(z1)), \), ENCARG(cons_app(z0, z1)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, \)) -> c11(APP(\, \), ENCARG(\))
   ENCARG(cons_app(e, \)) -> c11(APP(e, \), ENCARG(e))
   ENCARG(cons_app(., \)) -> c11(APP(., \), ENCARG(.))
   ENCARG(cons_app(/, \)) -> c11(APP(/, \), ENCARG(/))
   ENCARG(cons_app(map, \)) -> c11(APP(map, \), ENCARG(map))
   ENCARG(cons_app(nil, \)) -> c11(APP(nil, \), ENCARG(nil))
   ENCARG(cons_app(cons, \)) -> c11(APP(cons, \), ENCARG(cons))
   ENCARG(cons_app(filter, \)) -> c11(APP(filter, \), ENCARG(filter))
   ENCARG(cons_app(filter2, \)) -> c11(APP(filter2, \), ENCARG(filter2))
   ENCARG(cons_app(true, \)) -> c11(APP(true, \), ENCARG(true))
   ENCARG(cons_app(false, \)) -> c11(APP(false, \), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(\, \)) -> c11(APP(\, \), ENCARG(\))
   ENCARG(cons_app(filter2, \)) -> c11(APP(filter2, \), ENCARG(filter2))
   ENCARG(cons_app(nil, \)) -> c11(APP(nil, \), ENCARG(nil))
   ENCARG(cons_app(., \)) -> c11(APP(., \), ENCARG(.))
   ENCARG(cons_app(e, \)) -> c11(APP(e, \), ENCARG(e))
   ENCARG(cons_app(filter, \)) -> c11(APP(filter, \), ENCARG(filter))
   ENCARG(cons_app(map, \)) -> c11(APP(map, \), ENCARG(map))
   ENCARG(cons_app(/, \)) -> c11(APP(/, \), ENCARG(/))
   ENCARG(cons_app(false, \)) -> c11(APP(false, \), ENCARG(false))
   ENCARG(cons_app(true, \)) -> c11(APP(true, \), ENCARG(true))
   ENCARG(cons_app(cons, \)) -> c11(APP(cons, \), ENCARG(cons))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, e)) -> c11(APP(encArg(x0), e), ENCARG(x0)) by 
   ENCARG(cons_app(\, e)) -> c11(APP(\, e), ENCARG(\))
   ENCARG(cons_app(e, e)) -> c11(APP(e, e), ENCARG(e))
   ENCARG(cons_app(., e)) -> c11(APP(., e), ENCARG(.))
   ENCARG(cons_app(/, e)) -> c11(APP(/, e), ENCARG(/))
   ENCARG(cons_app(map, e)) -> c11(APP(map, e), ENCARG(map))
   ENCARG(cons_app(nil, e)) -> c11(APP(nil, e), ENCARG(nil))
   ENCARG(cons_app(cons, e)) -> c11(APP(cons, e), ENCARG(cons))
   ENCARG(cons_app(filter, e)) -> c11(APP(filter, e), ENCARG(filter))
   ENCARG(cons_app(filter2, e)) -> c11(APP(filter2, e), ENCARG(filter2))
   ENCARG(cons_app(true, e)) -> c11(APP(true, e), ENCARG(true))
   ENCARG(cons_app(false, e)) -> c11(APP(false, e), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), e)) -> c11(APP(app(encArg(z0), encArg(z1)), e), ENCARG(cons_app(z0, z1)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, e)) -> c11(APP(\, e), ENCARG(\))
   ENCARG(cons_app(e, e)) -> c11(APP(e, e), ENCARG(e))
   ENCARG(cons_app(., e)) -> c11(APP(., e), ENCARG(.))
   ENCARG(cons_app(/, e)) -> c11(APP(/, e), ENCARG(/))
   ENCARG(cons_app(map, e)) -> c11(APP(map, e), ENCARG(map))
   ENCARG(cons_app(nil, e)) -> c11(APP(nil, e), ENCARG(nil))
   ENCARG(cons_app(cons, e)) -> c11(APP(cons, e), ENCARG(cons))
   ENCARG(cons_app(filter, e)) -> c11(APP(filter, e), ENCARG(filter))
   ENCARG(cons_app(filter2, e)) -> c11(APP(filter2, e), ENCARG(filter2))
   ENCARG(cons_app(true, e)) -> c11(APP(true, e), ENCARG(true))
   ENCARG(cons_app(false, e)) -> c11(APP(false, e), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(false, e)) -> c11(APP(false, e), ENCARG(false))
   ENCARG(cons_app(nil, e)) -> c11(APP(nil, e), ENCARG(nil))
   ENCARG(cons_app(map, e)) -> c11(APP(map, e), ENCARG(map))
   ENCARG(cons_app(., e)) -> c11(APP(., e), ENCARG(.))
   ENCARG(cons_app(filter2, e)) -> c11(APP(filter2, e), ENCARG(filter2))
   ENCARG(cons_app(e, e)) -> c11(APP(e, e), ENCARG(e))
   ENCARG(cons_app(\, e)) -> c11(APP(\, e), ENCARG(\))
   ENCARG(cons_app(cons, e)) -> c11(APP(cons, e), ENCARG(cons))
   ENCARG(cons_app(true, e)) -> c11(APP(true, e), ENCARG(true))
   ENCARG(cons_app(filter, e)) -> c11(APP(filter, e), ENCARG(filter))
   ENCARG(cons_app(/, e)) -> c11(APP(/, e), ENCARG(/))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, .)) -> c11(APP(encArg(x0), .), ENCARG(x0)) by 
   ENCARG(cons_app(\, .)) -> c11(APP(\, .), ENCARG(\))
   ENCARG(cons_app(e, .)) -> c11(APP(e, .), ENCARG(e))
   ENCARG(cons_app(., .)) -> c11(APP(., .), ENCARG(.))
   ENCARG(cons_app(/, .)) -> c11(APP(/, .), ENCARG(/))
   ENCARG(cons_app(map, .)) -> c11(APP(map, .), ENCARG(map))
   ENCARG(cons_app(nil, .)) -> c11(APP(nil, .), ENCARG(nil))
   ENCARG(cons_app(cons, .)) -> c11(APP(cons, .), ENCARG(cons))
   ENCARG(cons_app(filter, .)) -> c11(APP(filter, .), ENCARG(filter))
   ENCARG(cons_app(filter2, .)) -> c11(APP(filter2, .), ENCARG(filter2))
   ENCARG(cons_app(true, .)) -> c11(APP(true, .), ENCARG(true))
   ENCARG(cons_app(false, .)) -> c11(APP(false, .), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), .)) -> c11(APP(app(encArg(z0), encArg(z1)), .), ENCARG(cons_app(z0, z1)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, .)) -> c11(APP(\, .), ENCARG(\))
   ENCARG(cons_app(e, .)) -> c11(APP(e, .), ENCARG(e))
   ENCARG(cons_app(., .)) -> c11(APP(., .), ENCARG(.))
   ENCARG(cons_app(/, .)) -> c11(APP(/, .), ENCARG(/))
   ENCARG(cons_app(map, .)) -> c11(APP(map, .), ENCARG(map))
   ENCARG(cons_app(nil, .)) -> c11(APP(nil, .), ENCARG(nil))
   ENCARG(cons_app(cons, .)) -> c11(APP(cons, .), ENCARG(cons))
   ENCARG(cons_app(filter, .)) -> c11(APP(filter, .), ENCARG(filter))
   ENCARG(cons_app(filter2, .)) -> c11(APP(filter2, .), ENCARG(filter2))
   ENCARG(cons_app(true, .)) -> c11(APP(true, .), ENCARG(true))
   ENCARG(cons_app(false, .)) -> c11(APP(false, .), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(nil, .)) -> c11(APP(nil, .), ENCARG(nil))
   ENCARG(cons_app(true, .)) -> c11(APP(true, .), ENCARG(true))
   ENCARG(cons_app(e, .)) -> c11(APP(e, .), ENCARG(e))
   ENCARG(cons_app(filter2, .)) -> c11(APP(filter2, .), ENCARG(filter2))
   ENCARG(cons_app(filter, .)) -> c11(APP(filter, .), ENCARG(filter))
   ENCARG(cons_app(/, .)) -> c11(APP(/, .), ENCARG(/))
   ENCARG(cons_app(., .)) -> c11(APP(., .), ENCARG(.))
   ENCARG(cons_app(cons, .)) -> c11(APP(cons, .), ENCARG(cons))
   ENCARG(cons_app(map, .)) -> c11(APP(map, .), ENCARG(map))
   ENCARG(cons_app(\, .)) -> c11(APP(\, .), ENCARG(\))
   ENCARG(cons_app(false, .)) -> c11(APP(false, .), ENCARG(false))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, /)) -> c11(APP(encArg(x0), /), ENCARG(x0)) by 
   ENCARG(cons_app(\, /)) -> c11(APP(\, /), ENCARG(\))
   ENCARG(cons_app(e, /)) -> c11(APP(e, /), ENCARG(e))
   ENCARG(cons_app(., /)) -> c11(APP(., /), ENCARG(.))
   ENCARG(cons_app(/, /)) -> c11(APP(/, /), ENCARG(/))
   ENCARG(cons_app(map, /)) -> c11(APP(map, /), ENCARG(map))
   ENCARG(cons_app(nil, /)) -> c11(APP(nil, /), ENCARG(nil))
   ENCARG(cons_app(cons, /)) -> c11(APP(cons, /), ENCARG(cons))
   ENCARG(cons_app(filter, /)) -> c11(APP(filter, /), ENCARG(filter))
   ENCARG(cons_app(filter2, /)) -> c11(APP(filter2, /), ENCARG(filter2))
   ENCARG(cons_app(true, /)) -> c11(APP(true, /), ENCARG(true))
   ENCARG(cons_app(false, /)) -> c11(APP(false, /), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), /)) -> c11(APP(app(encArg(z0), encArg(z1)), /), ENCARG(cons_app(z0, z1)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, /)) -> c11(APP(\, /), ENCARG(\))
   ENCARG(cons_app(e, /)) -> c11(APP(e, /), ENCARG(e))
   ENCARG(cons_app(., /)) -> c11(APP(., /), ENCARG(.))
   ENCARG(cons_app(/, /)) -> c11(APP(/, /), ENCARG(/))
   ENCARG(cons_app(map, /)) -> c11(APP(map, /), ENCARG(map))
   ENCARG(cons_app(nil, /)) -> c11(APP(nil, /), ENCARG(nil))
   ENCARG(cons_app(cons, /)) -> c11(APP(cons, /), ENCARG(cons))
   ENCARG(cons_app(filter, /)) -> c11(APP(filter, /), ENCARG(filter))
   ENCARG(cons_app(filter2, /)) -> c11(APP(filter2, /), ENCARG(filter2))
   ENCARG(cons_app(true, /)) -> c11(APP(true, /), ENCARG(true))
   ENCARG(cons_app(false, /)) -> c11(APP(false, /), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(true, /)) -> c11(APP(true, /), ENCARG(true))
   ENCARG(cons_app(map, /)) -> c11(APP(map, /), ENCARG(map))
   ENCARG(cons_app(filter, /)) -> c11(APP(filter, /), ENCARG(filter))
   ENCARG(cons_app(/, /)) -> c11(APP(/, /), ENCARG(/))
   ENCARG(cons_app(e, /)) -> c11(APP(e, /), ENCARG(e))
   ENCARG(cons_app(filter2, /)) -> c11(APP(filter2, /), ENCARG(filter2))
   ENCARG(cons_app(nil, /)) -> c11(APP(nil, /), ENCARG(nil))
   ENCARG(cons_app(., /)) -> c11(APP(., /), ENCARG(.))
   ENCARG(cons_app(cons, /)) -> c11(APP(cons, /), ENCARG(cons))
   ENCARG(cons_app(\, /)) -> c11(APP(\, /), ENCARG(\))
   ENCARG(cons_app(false, /)) -> c11(APP(false, /), ENCARG(false))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, map)) -> c11(APP(encArg(x0), map), ENCARG(x0)) by 
   ENCARG(cons_app(\, map)) -> c11(APP(\, map), ENCARG(\))
   ENCARG(cons_app(e, map)) -> c11(APP(e, map), ENCARG(e))
   ENCARG(cons_app(., map)) -> c11(APP(., map), ENCARG(.))
   ENCARG(cons_app(/, map)) -> c11(APP(/, map), ENCARG(/))
   ENCARG(cons_app(map, map)) -> c11(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c11(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c11(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c11(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c11(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(true, map)) -> c11(APP(true, map), ENCARG(true))
   ENCARG(cons_app(false, map)) -> c11(APP(false, map), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), map)) -> c11(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1)))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, map)) -> c11(APP(\, map), ENCARG(\))
   ENCARG(cons_app(e, map)) -> c11(APP(e, map), ENCARG(e))
   ENCARG(cons_app(., map)) -> c11(APP(., map), ENCARG(.))
   ENCARG(cons_app(/, map)) -> c11(APP(/, map), ENCARG(/))
   ENCARG(cons_app(map, map)) -> c11(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c11(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c11(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c11(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c11(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(true, map)) -> c11(APP(true, map), ENCARG(true))
   ENCARG(cons_app(false, map)) -> c11(APP(false, map), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(nil, map)) -> c11(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(., map)) -> c11(APP(., map), ENCARG(.))
   ENCARG(cons_app(true, map)) -> c11(APP(true, map), ENCARG(true))
   ENCARG(cons_app(filter2, map)) -> c11(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(filter, map)) -> c11(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(/, map)) -> c11(APP(/, map), ENCARG(/))
   ENCARG(cons_app(\, map)) -> c11(APP(\, map), ENCARG(\))
   ENCARG(cons_app(false, map)) -> c11(APP(false, map), ENCARG(false))
   ENCARG(cons_app(e, map)) -> c11(APP(e, map), ENCARG(e))
   ENCARG(cons_app(cons, map)) -> c11(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(map, map)) -> c11(APP(map, map), ENCARG(map))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c11(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(\, nil)) -> c11(APP(\, nil), ENCARG(\))
   ENCARG(cons_app(e, nil)) -> c11(APP(e, nil), ENCARG(e))
   ENCARG(cons_app(., nil)) -> c11(APP(., nil), ENCARG(.))
   ENCARG(cons_app(/, nil)) -> c11(APP(/, nil), ENCARG(/))
   ENCARG(cons_app(map, nil)) -> c11(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c11(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c11(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c11(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c11(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(true, nil)) -> c11(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c11(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c11(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, nil)) -> c11(APP(\, nil), ENCARG(\))
   ENCARG(cons_app(e, nil)) -> c11(APP(e, nil), ENCARG(e))
   ENCARG(cons_app(., nil)) -> c11(APP(., nil), ENCARG(.))
   ENCARG(cons_app(/, nil)) -> c11(APP(/, nil), ENCARG(/))
   ENCARG(cons_app(map, nil)) -> c11(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c11(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c11(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c11(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c11(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(true, nil)) -> c11(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c11(APP(false, nil), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(., nil)) -> c11(APP(., nil), ENCARG(.))
   ENCARG(cons_app(map, nil)) -> c11(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(filter, nil)) -> c11(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(/, nil)) -> c11(APP(/, nil), ENCARG(/))
   ENCARG(cons_app(false, nil)) -> c11(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(true, nil)) -> c11(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(e, nil)) -> c11(APP(e, nil), ENCARG(e))
   ENCARG(cons_app(\, nil)) -> c11(APP(\, nil), ENCARG(\))
   ENCARG(cons_app(filter2, nil)) -> c11(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(cons, nil)) -> c11(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(nil, nil)) -> c11(APP(nil, nil), ENCARG(nil))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c11(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(\, cons)) -> c11(APP(\, cons), ENCARG(\))
   ENCARG(cons_app(e, cons)) -> c11(APP(e, cons), ENCARG(e))
   ENCARG(cons_app(., cons)) -> c11(APP(., cons), ENCARG(.))
   ENCARG(cons_app(/, cons)) -> c11(APP(/, cons), ENCARG(/))
   ENCARG(cons_app(map, cons)) -> c11(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c11(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c11(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c11(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c11(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(true, cons)) -> c11(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c11(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c11(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, cons)) -> c11(APP(\, cons), ENCARG(\))
   ENCARG(cons_app(e, cons)) -> c11(APP(e, cons), ENCARG(e))
   ENCARG(cons_app(., cons)) -> c11(APP(., cons), ENCARG(.))
   ENCARG(cons_app(/, cons)) -> c11(APP(/, cons), ENCARG(/))
   ENCARG(cons_app(map, cons)) -> c11(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c11(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c11(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c11(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c11(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(true, cons)) -> c11(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c11(APP(false, cons), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(cons, cons)) -> c11(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(\, cons)) -> c11(APP(\, cons), ENCARG(\))
   ENCARG(cons_app(true, cons)) -> c11(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(filter2, cons)) -> c11(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(false, cons)) -> c11(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(e, cons)) -> c11(APP(e, cons), ENCARG(e))
   ENCARG(cons_app(nil, cons)) -> c11(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(map, cons)) -> c11(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(filter, cons)) -> c11(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(/, cons)) -> c11(APP(/, cons), ENCARG(/))
   ENCARG(cons_app(., cons)) -> c11(APP(., cons), ENCARG(.))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c11(APP(encArg(x0), filter), ENCARG(x0)) by 
   ENCARG(cons_app(\, filter)) -> c11(APP(\, filter), ENCARG(\))
   ENCARG(cons_app(e, filter)) -> c11(APP(e, filter), ENCARG(e))
   ENCARG(cons_app(., filter)) -> c11(APP(., filter), ENCARG(.))
   ENCARG(cons_app(/, filter)) -> c11(APP(/, filter), ENCARG(/))
   ENCARG(cons_app(map, filter)) -> c11(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c11(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c11(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c11(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c11(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(true, filter)) -> c11(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(false, filter)) -> c11(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), filter)) -> c11(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, filter)) -> c11(APP(\, filter), ENCARG(\))
   ENCARG(cons_app(e, filter)) -> c11(APP(e, filter), ENCARG(e))
   ENCARG(cons_app(., filter)) -> c11(APP(., filter), ENCARG(.))
   ENCARG(cons_app(/, filter)) -> c11(APP(/, filter), ENCARG(/))
   ENCARG(cons_app(map, filter)) -> c11(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c11(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c11(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c11(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c11(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(true, filter)) -> c11(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(false, filter)) -> c11(APP(false, filter), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(cons, filter)) -> c11(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(map, filter)) -> c11(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(false, filter)) -> c11(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(filter, filter)) -> c11(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(/, filter)) -> c11(APP(/, filter), ENCARG(/))
   ENCARG(cons_app(e, filter)) -> c11(APP(e, filter), ENCARG(e))
   ENCARG(cons_app(\, filter)) -> c11(APP(\, filter), ENCARG(\))
   ENCARG(cons_app(true, filter)) -> c11(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(., filter)) -> c11(APP(., filter), ENCARG(.))
   ENCARG(cons_app(filter2, filter)) -> c11(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(nil, filter)) -> c11(APP(nil, filter), ENCARG(nil))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter2)) -> c11(APP(encArg(x0), filter2), ENCARG(x0)) by 
   ENCARG(cons_app(\, filter2)) -> c11(APP(\, filter2), ENCARG(\))
   ENCARG(cons_app(e, filter2)) -> c11(APP(e, filter2), ENCARG(e))
   ENCARG(cons_app(., filter2)) -> c11(APP(., filter2), ENCARG(.))
   ENCARG(cons_app(/, filter2)) -> c11(APP(/, filter2), ENCARG(/))
   ENCARG(cons_app(map, filter2)) -> c11(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c11(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c11(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c11(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c11(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(true, filter2)) -> c11(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(false, filter2)) -> c11(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), filter2)) -> c11(APP(app(encArg(z0), encArg(z1)), filter2), ENCARG(cons_app(z0, z1)))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, filter2)) -> c11(APP(\, filter2), ENCARG(\))
   ENCARG(cons_app(e, filter2)) -> c11(APP(e, filter2), ENCARG(e))
   ENCARG(cons_app(., filter2)) -> c11(APP(., filter2), ENCARG(.))
   ENCARG(cons_app(/, filter2)) -> c11(APP(/, filter2), ENCARG(/))
   ENCARG(cons_app(map, filter2)) -> c11(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c11(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c11(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c11(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c11(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(true, filter2)) -> c11(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(false, filter2)) -> c11(APP(false, filter2), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(false, filter2)) -> c11(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(filter2, filter2)) -> c11(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(., filter2)) -> c11(APP(., filter2), ENCARG(.))
   ENCARG(cons_app(nil, filter2)) -> c11(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(map, filter2)) -> c11(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(filter, filter2)) -> c11(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(/, filter2)) -> c11(APP(/, filter2), ENCARG(/))
   ENCARG(cons_app(cons, filter2)) -> c11(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(\, filter2)) -> c11(APP(\, filter2), ENCARG(\))
   ENCARG(cons_app(true, filter2)) -> c11(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(e, filter2)) -> c11(APP(e, filter2), ENCARG(e))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, true)) -> c11(APP(encArg(x0), true), ENCARG(x0)) by 
   ENCARG(cons_app(\, true)) -> c11(APP(\, true), ENCARG(\))
   ENCARG(cons_app(e, true)) -> c11(APP(e, true), ENCARG(e))
   ENCARG(cons_app(., true)) -> c11(APP(., true), ENCARG(.))
   ENCARG(cons_app(/, true)) -> c11(APP(/, true), ENCARG(/))
   ENCARG(cons_app(map, true)) -> c11(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c11(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c11(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c11(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c11(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(true, true)) -> c11(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c11(APP(false, true), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), true)) -> c11(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, true)) -> c11(APP(\, true), ENCARG(\))
   ENCARG(cons_app(e, true)) -> c11(APP(e, true), ENCARG(e))
   ENCARG(cons_app(., true)) -> c11(APP(., true), ENCARG(.))
   ENCARG(cons_app(/, true)) -> c11(APP(/, true), ENCARG(/))
   ENCARG(cons_app(map, true)) -> c11(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c11(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c11(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c11(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c11(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(true, true)) -> c11(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c11(APP(false, true), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(false, true)) -> c11(APP(false, true), ENCARG(false))
   ENCARG(cons_app(map, true)) -> c11(APP(map, true), ENCARG(map))
   ENCARG(cons_app(., true)) -> c11(APP(., true), ENCARG(.))
   ENCARG(cons_app(cons, true)) -> c11(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(e, true)) -> c11(APP(e, true), ENCARG(e))
   ENCARG(cons_app(true, true)) -> c11(APP(true, true), ENCARG(true))
   ENCARG(cons_app(\, true)) -> c11(APP(\, true), ENCARG(\))
   ENCARG(cons_app(filter, true)) -> c11(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(/, true)) -> c11(APP(/, true), ENCARG(/))
   ENCARG(cons_app(filter2, true)) -> c11(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(nil, true)) -> c11(APP(nil, true), ENCARG(nil))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_2, c11_1, c39_2, c39_1, c_1, c11_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, false)) -> c11(APP(encArg(x0), false), ENCARG(x0)) by 
   ENCARG(cons_app(\, false)) -> c11(APP(\, false), ENCARG(\))
   ENCARG(cons_app(e, false)) -> c11(APP(e, false), ENCARG(e))
   ENCARG(cons_app(., false)) -> c11(APP(., false), ENCARG(.))
   ENCARG(cons_app(/, false)) -> c11(APP(/, false), ENCARG(/))
   ENCARG(cons_app(map, false)) -> c11(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c11(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c11(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c11(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c11(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(true, false)) -> c11(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c11(APP(false, false), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), false)) -> c11(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(\, false)) -> c11(APP(\, false), ENCARG(\))
   ENCARG(cons_app(e, false)) -> c11(APP(e, false), ENCARG(e))
   ENCARG(cons_app(., false)) -> c11(APP(., false), ENCARG(.))
   ENCARG(cons_app(/, false)) -> c11(APP(/, false), ENCARG(/))
   ENCARG(cons_app(map, false)) -> c11(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c11(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c11(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c11(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c11(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(true, false)) -> c11(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c11(APP(false, false), ENCARG(false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCARG(cons_app(false, false)) -> c11(APP(false, false), ENCARG(false))
   ENCARG(cons_app(nil, false)) -> c11(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(\, false)) -> c11(APP(\, false), ENCARG(\))
   ENCARG(cons_app(true, false)) -> c11(APP(true, false), ENCARG(true))
   ENCARG(cons_app(filter2, false)) -> c11(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(cons, false)) -> c11(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(e, false)) -> c11(APP(e, false), ENCARG(e))
   ENCARG(cons_app(filter, false)) -> c11(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(/, false)) -> c11(APP(/, false), ENCARG(/))
   ENCARG(cons_app(., false)) -> c11(APP(., false), ENCARG(.))
   ENCARG(cons_app(map, false)) -> c11(APP(map, false), ENCARG(map))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(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)) -> c39(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)) -> c39(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(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, e), app(\, z0)), z0), x2)), app(filter, app(\, z0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, e), app(/, z0)), z0), x2)), app(filter, app(/, z0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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)) -> c39(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(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, e), app(\, z0)), z0), x2)), app(filter, app(\, z0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, e), app(/, z0)), z0), x2)), app(filter, app(/, z0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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)) -> c39(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(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, e), app(\, z0)), z0), x2)), app(filter, app(\, z0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, e), app(/, z0)), z0), x2)), app(filter, app(/, z0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c39(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(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, \) -> c(APP(encArg(x0), \))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, \) -> c(APP(encArg(x0), \)) by 
   ENCODE_APP(\, \) -> c(APP(\, \))
   ENCODE_APP(e, \) -> c(APP(e, \))
   ENCODE_APP(., \) -> c(APP(., \))
   ENCODE_APP(/, \) -> c(APP(/, \))
   ENCODE_APP(map, \) -> c(APP(map, \))
   ENCODE_APP(nil, \) -> c(APP(nil, \))
   ENCODE_APP(cons, \) -> c(APP(cons, \))
   ENCODE_APP(filter, \) -> c(APP(filter, \))
   ENCODE_APP(filter2, \) -> c(APP(filter2, \))
   ENCODE_APP(true, \) -> c(APP(true, \))
   ENCODE_APP(false, \) -> c(APP(false, \))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(\, \) -> c(APP(\, \))
   ENCODE_APP(e, \) -> c(APP(e, \))
   ENCODE_APP(., \) -> c(APP(., \))
   ENCODE_APP(/, \) -> c(APP(/, \))
   ENCODE_APP(map, \) -> c(APP(map, \))
   ENCODE_APP(nil, \) -> c(APP(nil, \))
   ENCODE_APP(cons, \) -> c(APP(cons, \))
   ENCODE_APP(filter, \) -> c(APP(filter, \))
   ENCODE_APP(filter2, \) -> c(APP(filter2, \))
   ENCODE_APP(true, \) -> c(APP(true, \))
   ENCODE_APP(false, \) -> c(APP(false, \))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(e, \) -> c(APP(e, \))
   ENCODE_APP(filter2, \) -> c(APP(filter2, \))
   ENCODE_APP(nil, \) -> c(APP(nil, \))
   ENCODE_APP(\, \) -> c(APP(\, \))
   ENCODE_APP(false, \) -> c(APP(false, \))
   ENCODE_APP(filter, \) -> c(APP(filter, \))
   ENCODE_APP(map, \) -> c(APP(map, \))
   ENCODE_APP(/, \) -> c(APP(/, \))
   ENCODE_APP(true, \) -> c(APP(true, \))
   ENCODE_APP(cons, \) -> c(APP(cons, \))
   ENCODE_APP(., \) -> c(APP(., \))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, e) -> c(APP(encArg(x0), e))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, e) -> c(APP(encArg(x0), e)) by 
   ENCODE_APP(\, e) -> c(APP(\, e))
   ENCODE_APP(e, e) -> c(APP(e, e))
   ENCODE_APP(., e) -> c(APP(., e))
   ENCODE_APP(/, e) -> c(APP(/, e))
   ENCODE_APP(map, e) -> c(APP(map, e))
   ENCODE_APP(nil, e) -> c(APP(nil, e))
   ENCODE_APP(cons, e) -> c(APP(cons, e))
   ENCODE_APP(filter, e) -> c(APP(filter, e))
   ENCODE_APP(filter2, e) -> c(APP(filter2, e))
   ENCODE_APP(true, e) -> c(APP(true, e))
   ENCODE_APP(false, e) -> c(APP(false, e))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(\, e) -> c(APP(\, e))
   ENCODE_APP(e, e) -> c(APP(e, e))
   ENCODE_APP(., e) -> c(APP(., e))
   ENCODE_APP(/, e) -> c(APP(/, e))
   ENCODE_APP(map, e) -> c(APP(map, e))
   ENCODE_APP(nil, e) -> c(APP(nil, e))
   ENCODE_APP(cons, e) -> c(APP(cons, e))
   ENCODE_APP(filter, e) -> c(APP(filter, e))
   ENCODE_APP(filter2, e) -> c(APP(filter2, e))
   ENCODE_APP(true, e) -> c(APP(true, e))
   ENCODE_APP(false, e) -> c(APP(false, e))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(filter2, e) -> c(APP(filter2, e))
   ENCODE_APP(nil, e) -> c(APP(nil, e))
   ENCODE_APP(map, e) -> c(APP(map, e))
   ENCODE_APP(., e) -> c(APP(., e))
   ENCODE_APP(false, e) -> c(APP(false, e))
   ENCODE_APP(e, e) -> c(APP(e, e))
   ENCODE_APP(true, e) -> c(APP(true, e))
   ENCODE_APP(filter, e) -> c(APP(filter, e))
   ENCODE_APP(/, e) -> c(APP(/, e))
   ENCODE_APP(\, e) -> c(APP(\, e))
   ENCODE_APP(cons, e) -> c(APP(cons, e))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, .) -> c(APP(encArg(x0), .))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) by 
   ENCODE_APP(\, .) -> c(APP(\, .))
   ENCODE_APP(e, .) -> c(APP(e, .))
   ENCODE_APP(., .) -> c(APP(., .))
   ENCODE_APP(/, .) -> c(APP(/, .))
   ENCODE_APP(map, .) -> c(APP(map, .))
   ENCODE_APP(nil, .) -> c(APP(nil, .))
   ENCODE_APP(cons, .) -> c(APP(cons, .))
   ENCODE_APP(filter, .) -> c(APP(filter, .))
   ENCODE_APP(filter2, .) -> c(APP(filter2, .))
   ENCODE_APP(true, .) -> c(APP(true, .))
   ENCODE_APP(false, .) -> c(APP(false, .))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(\, .) -> c(APP(\, .))
   ENCODE_APP(e, .) -> c(APP(e, .))
   ENCODE_APP(., .) -> c(APP(., .))
   ENCODE_APP(/, .) -> c(APP(/, .))
   ENCODE_APP(map, .) -> c(APP(map, .))
   ENCODE_APP(nil, .) -> c(APP(nil, .))
   ENCODE_APP(cons, .) -> c(APP(cons, .))
   ENCODE_APP(filter, .) -> c(APP(filter, .))
   ENCODE_APP(filter2, .) -> c(APP(filter2, .))
   ENCODE_APP(true, .) -> c(APP(true, .))
   ENCODE_APP(false, .) -> c(APP(false, .))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(cons, .) -> c(APP(cons, .))
   ENCODE_APP(., .) -> c(APP(., .))
   ENCODE_APP(nil, .) -> c(APP(nil, .))
   ENCODE_APP(false, .) -> c(APP(false, .))
   ENCODE_APP(filter2, .) -> c(APP(filter2, .))
   ENCODE_APP(\, .) -> c(APP(\, .))
   ENCODE_APP(map, .) -> c(APP(map, .))
   ENCODE_APP(e, .) -> c(APP(e, .))
   ENCODE_APP(true, .) -> c(APP(true, .))
   ENCODE_APP(filter, .) -> c(APP(filter, .))
   ENCODE_APP(/, .) -> c(APP(/, .))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, /) -> c(APP(encArg(x0), /))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, /) -> c(APP(encArg(x0), /)) by 
   ENCODE_APP(\, /) -> c(APP(\, /))
   ENCODE_APP(e, /) -> c(APP(e, /))
   ENCODE_APP(., /) -> c(APP(., /))
   ENCODE_APP(/, /) -> c(APP(/, /))
   ENCODE_APP(map, /) -> c(APP(map, /))
   ENCODE_APP(nil, /) -> c(APP(nil, /))
   ENCODE_APP(cons, /) -> c(APP(cons, /))
   ENCODE_APP(filter, /) -> c(APP(filter, /))
   ENCODE_APP(filter2, /) -> c(APP(filter2, /))
   ENCODE_APP(true, /) -> c(APP(true, /))
   ENCODE_APP(false, /) -> c(APP(false, /))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(\, /) -> c(APP(\, /))
   ENCODE_APP(e, /) -> c(APP(e, /))
   ENCODE_APP(., /) -> c(APP(., /))
   ENCODE_APP(/, /) -> c(APP(/, /))
   ENCODE_APP(map, /) -> c(APP(map, /))
   ENCODE_APP(nil, /) -> c(APP(nil, /))
   ENCODE_APP(cons, /) -> c(APP(cons, /))
   ENCODE_APP(filter, /) -> c(APP(filter, /))
   ENCODE_APP(filter2, /) -> c(APP(filter2, /))
   ENCODE_APP(true, /) -> c(APP(true, /))
   ENCODE_APP(false, /) -> c(APP(false, /))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(false, /) -> c(APP(false, /))
   ENCODE_APP(filter2, /) -> c(APP(filter2, /))
   ENCODE_APP(cons, /) -> c(APP(cons, /))
   ENCODE_APP(\, /) -> c(APP(\, /))
   ENCODE_APP(true, /) -> c(APP(true, /))
   ENCODE_APP(nil, /) -> c(APP(nil, /))
   ENCODE_APP(e, /) -> c(APP(e, /))
   ENCODE_APP(map, /) -> c(APP(map, /))
   ENCODE_APP(filter, /) -> c(APP(filter, /))
   ENCODE_APP(/, /) -> c(APP(/, /))
   ENCODE_APP(., /) -> c(APP(., /))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) by 
   ENCODE_APP(\, map) -> c(APP(\, map))
   ENCODE_APP(e, map) -> c(APP(e, map))
   ENCODE_APP(., map) -> c(APP(., map))
   ENCODE_APP(/, map) -> c(APP(/, 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))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(\, map) -> c(APP(\, map))
   ENCODE_APP(e, map) -> c(APP(e, map))
   ENCODE_APP(., map) -> c(APP(., map))
   ENCODE_APP(/, map) -> c(APP(/, 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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(cons, map) -> c(APP(cons, map))
   ENCODE_APP(e, map) -> c(APP(e, map))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(false, map) -> c(APP(false, map))
   ENCODE_APP(filter, map) -> c(APP(filter, map))
   ENCODE_APP(/, map) -> c(APP(/, map))
   ENCODE_APP(\, map) -> c(APP(\, map))
   ENCODE_APP(true, map) -> c(APP(true, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(filter2, map) -> c(APP(filter2, map))
   ENCODE_APP(., map) -> c(APP(., map))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by 
   ENCODE_APP(\, nil) -> c(APP(\, nil))
   ENCODE_APP(e, nil) -> c(APP(e, nil))
   ENCODE_APP(., nil) -> c(APP(., nil))
   ENCODE_APP(/, nil) -> c(APP(/, 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))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(\, nil) -> c(APP(\, nil))
   ENCODE_APP(e, nil) -> c(APP(e, nil))
   ENCODE_APP(., nil) -> c(APP(., nil))
   ENCODE_APP(/, nil) -> c(APP(/, 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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(e, nil) -> c(APP(e, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(filter2, nil) -> c(APP(filter2, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(/, nil) -> c(APP(/, nil))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(., nil) -> c(APP(., nil))
   ENCODE_APP(\, nil) -> c(APP(\, nil))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) by 
   ENCODE_APP(\, cons) -> c(APP(\, cons))
   ENCODE_APP(e, cons) -> c(APP(e, cons))
   ENCODE_APP(., cons) -> c(APP(., cons))
   ENCODE_APP(/, cons) -> c(APP(/, 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))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   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) -> c(APP(\, cons))
   ENCODE_APP(e, cons) -> c(APP(e, cons))
   ENCODE_APP(., cons) -> c(APP(., cons))
   ENCODE_APP(/, cons) -> c(APP(/, 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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(e, cons) -> c(APP(e, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(map, cons) -> c(APP(map, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(/, cons) -> c(APP(/, cons))
   ENCODE_APP(., cons) -> c(APP(., cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(filter2, cons) -> c(APP(filter2, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(\, cons) -> c(APP(\, cons))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) by 
   ENCODE_APP(\, filter) -> c(APP(\, filter))
   ENCODE_APP(e, filter) -> c(APP(e, filter))
   ENCODE_APP(., filter) -> c(APP(., filter))
   ENCODE_APP(/, filter) -> c(APP(/, filter))
   ENCODE_APP(map, filter) -> c(APP(map, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(filter2, filter) -> c(APP(filter2, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(\, filter) -> c(APP(\, filter))
   ENCODE_APP(e, filter) -> c(APP(e, filter))
   ENCODE_APP(., filter) -> c(APP(., filter))
   ENCODE_APP(/, filter) -> c(APP(/, filter))
   ENCODE_APP(map, filter) -> c(APP(map, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(filter2, filter) -> c(APP(filter2, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(filter2, filter) -> c(APP(filter2, filter))
   ENCODE_APP(map, filter) -> c(APP(map, filter))
   ENCODE_APP(., filter) -> c(APP(., filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(/, filter) -> c(APP(/, filter))
   ENCODE_APP(\, filter) -> c(APP(\, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(e, filter) -> c(APP(e, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) by 
   ENCODE_APP(\, filter2) -> c(APP(\, filter2))
   ENCODE_APP(e, filter2) -> c(APP(e, filter2))
   ENCODE_APP(., filter2) -> c(APP(., filter2))
   ENCODE_APP(/, filter2) -> c(APP(/, filter2))
   ENCODE_APP(map, filter2) -> c(APP(map, filter2))
   ENCODE_APP(nil, filter2) -> c(APP(nil, filter2))
   ENCODE_APP(cons, filter2) -> c(APP(cons, filter2))
   ENCODE_APP(filter, filter2) -> c(APP(filter, filter2))
   ENCODE_APP(filter2, filter2) -> c(APP(filter2, filter2))
   ENCODE_APP(true, filter2) -> c(APP(true, filter2))
   ENCODE_APP(false, filter2) -> c(APP(false, filter2))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(\, filter2) -> c(APP(\, filter2))
   ENCODE_APP(e, filter2) -> c(APP(e, filter2))
   ENCODE_APP(., filter2) -> c(APP(., filter2))
   ENCODE_APP(/, filter2) -> c(APP(/, filter2))
   ENCODE_APP(map, filter2) -> c(APP(map, filter2))
   ENCODE_APP(nil, filter2) -> c(APP(nil, filter2))
   ENCODE_APP(cons, filter2) -> c(APP(cons, filter2))
   ENCODE_APP(filter, filter2) -> c(APP(filter, filter2))
   ENCODE_APP(filter2, filter2) -> c(APP(filter2, filter2))
   ENCODE_APP(true, filter2) -> c(APP(true, filter2))
   ENCODE_APP(false, filter2) -> c(APP(false, filter2))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(nil, filter2) -> c(APP(nil, filter2))
   ENCODE_APP(., filter2) -> c(APP(., filter2))
   ENCODE_APP(filter2, filter2) -> c(APP(filter2, filter2))
   ENCODE_APP(false, filter2) -> c(APP(false, filter2))
   ENCODE_APP(map, filter2) -> c(APP(map, filter2))
   ENCODE_APP(cons, filter2) -> c(APP(cons, filter2))
   ENCODE_APP(true, filter2) -> c(APP(true, filter2))
   ENCODE_APP(filter, filter2) -> c(APP(filter, filter2))
   ENCODE_APP(/, filter2) -> c(APP(/, filter2))
   ENCODE_APP(e, filter2) -> c(APP(e, filter2))
   ENCODE_APP(\, filter2) -> c(APP(\, filter2))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) by 
   ENCODE_APP(\, true) -> c(APP(\, true))
   ENCODE_APP(e, true) -> c(APP(e, true))
   ENCODE_APP(., true) -> c(APP(., true))
   ENCODE_APP(/, true) -> c(APP(/, true))
   ENCODE_APP(map, true) -> c(APP(map, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(filter, true) -> c(APP(filter, true))
   ENCODE_APP(filter2, true) -> c(APP(filter2, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(\, true) -> c(APP(\, true))
   ENCODE_APP(e, true) -> c(APP(e, true))
   ENCODE_APP(., true) -> c(APP(., true))
   ENCODE_APP(/, true) -> c(APP(/, true))
   ENCODE_APP(map, true) -> c(APP(map, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(filter, true) -> c(APP(filter, true))
   ENCODE_APP(filter2, true) -> c(APP(filter2, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(., true) -> c(APP(., true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(map, true) -> c(APP(map, true))
   ENCODE_APP(filter2, true) -> c(APP(filter2, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(filter, true) -> c(APP(filter, true))
   ENCODE_APP(/, true) -> c(APP(/, true))
   ENCODE_APP(\, true) -> c(APP(\, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(e, true) -> c(APP(e, true))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) by 
   ENCODE_APP(\, false) -> c(APP(\, false))
   ENCODE_APP(e, false) -> c(APP(e, false))
   ENCODE_APP(., false) -> c(APP(., false))
   ENCODE_APP(/, false) -> c(APP(/, false))
   ENCODE_APP(map, false) -> c(APP(map, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(filter, false) -> c(APP(filter, false))
   ENCODE_APP(filter2, false) -> c(APP(filter2, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(\, false) -> c(APP(\, false))
   ENCODE_APP(e, false) -> c(APP(e, false))
   ENCODE_APP(., false) -> c(APP(., false))
   ENCODE_APP(/, false) -> c(APP(/, false))
   ENCODE_APP(map, false) -> c(APP(map, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(filter, false) -> c(APP(filter, false))
   ENCODE_APP(filter2, false) -> c(APP(filter2, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(\, false) -> c(APP(\, false))
   ENCODE_APP(e, false) -> c(APP(e, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(filter2, false) -> c(APP(filter2, false))
   ENCODE_APP(filter, false) -> c(APP(filter, false))
   ENCODE_APP(/, false) -> c(APP(/, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(., false) -> c(APP(., false))
   ENCODE_APP(map, false) -> c(APP(map, false))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) by 
   ENCODE_APP(x0, cons_app(x1, \)) -> c(APP(encArg(x0), app(encArg(x1), \)))
   ENCODE_APP(x0, cons_app(x1, e)) -> c(APP(encArg(x0), app(encArg(x1), e)))
   ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .)))
   ENCODE_APP(x0, cons_app(x1, /)) -> c(APP(encArg(x0), app(encArg(x1), /)))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(\, x2)) -> c(APP(encArg(x0), app(\, encArg(x2))))
   ENCODE_APP(x0, cons_app(e, x2)) -> c(APP(encArg(x0), app(e, encArg(x2))))
   ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2))))
   ENCODE_APP(x0, cons_app(/, x2)) -> c(APP(encArg(x0), app(/, encArg(x2))))
   ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(\, cons_app(x1, x2)) -> c(APP(\, app(encArg(x1), encArg(x2))))
   ENCODE_APP(e, cons_app(x1, x2)) -> c(APP(e, app(encArg(x1), encArg(x2))))
   ENCODE_APP(., cons_app(x1, x2)) -> c(APP(., app(encArg(x1), encArg(x2))))
   ENCODE_APP(/, cons_app(x1, x2)) -> c(APP(/, app(encArg(x1), encArg(x2))))
   ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter2, cons_app(x1, x2)) -> c(APP(filter2, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(x0, cons_app(x1, \)) -> c(APP(encArg(x0), app(encArg(x1), \)))
   ENCODE_APP(x0, cons_app(x1, e)) -> c(APP(encArg(x0), app(encArg(x1), e)))
   ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .)))
   ENCODE_APP(x0, cons_app(x1, /)) -> c(APP(encArg(x0), app(encArg(x1), /)))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(\, x2)) -> c(APP(encArg(x0), app(\, encArg(x2))))
   ENCODE_APP(x0, cons_app(e, x2)) -> c(APP(encArg(x0), app(e, encArg(x2))))
   ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2))))
   ENCODE_APP(x0, cons_app(/, x2)) -> c(APP(encArg(x0), app(/, encArg(x2))))
   ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(\, cons_app(x1, x2)) -> c(APP(\, app(encArg(x1), encArg(x2))))
   ENCODE_APP(e, cons_app(x1, x2)) -> c(APP(e, app(encArg(x1), encArg(x2))))
   ENCODE_APP(., cons_app(x1, x2)) -> c(APP(., app(encArg(x1), encArg(x2))))
   ENCODE_APP(/, cons_app(x1, x2)) -> c(APP(/, app(encArg(x1), encArg(x2))))
   ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter2, cons_app(x1, x2)) -> c(APP(filter2, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(e, cons_app(x1, x2)) -> c(APP(e, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(\, cons_app(x1, x2)) -> c(APP(\, app(encArg(x1), encArg(x2))))
   ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter2, cons_app(x1, x2)) -> c(APP(filter2, app(encArg(x1), encArg(x2))))
   ENCODE_APP(., cons_app(x1, x2)) -> c(APP(., app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(/, cons_app(x1, x2)) -> c(APP(/, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(x0, cons_app(x1, \)) -> c(APP(encArg(x0), app(encArg(x1), \)))
   ENCODE_APP(x0, cons_app(x1, e)) -> c(APP(encArg(x0), app(encArg(x1), e)))
   ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .)))
   ENCODE_APP(x0, cons_app(x1, /)) -> c(APP(encArg(x0), app(encArg(x1), /)))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(\, x2)) -> c(APP(encArg(x0), app(\, encArg(x2))))
   ENCODE_APP(x0, cons_app(e, x2)) -> c(APP(encArg(x0), app(e, encArg(x2))))
   ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2))))
   ENCODE_APP(x0, cons_app(/, x2)) -> c(APP(encArg(x0), app(/, encArg(x2))))
   ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c_1, c11_3, c11_2


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) by 
   ENCODE_APP(cons_app(x0, x1), \) -> c(APP(app(encArg(x0), encArg(x1)), \))
   ENCODE_APP(cons_app(x0, x1), e) -> c(APP(app(encArg(x0), encArg(x1)), e))
   ENCODE_APP(cons_app(x0, x1), .) -> c(APP(app(encArg(x0), encArg(x1)), .))
   ENCODE_APP(cons_app(x0, x1), /) -> c(APP(app(encArg(x0), encArg(x1)), /))
   ENCODE_APP(cons_app(x0, x1), map) -> c(APP(app(encArg(x0), encArg(x1)), map))
   ENCODE_APP(cons_app(x0, x1), nil) -> c(APP(app(encArg(x0), encArg(x1)), nil))
   ENCODE_APP(cons_app(x0, x1), cons) -> c(APP(app(encArg(x0), encArg(x1)), cons))
   ENCODE_APP(cons_app(x0, x1), filter) -> c(APP(app(encArg(x0), encArg(x1)), filter))
   ENCODE_APP(cons_app(x0, x1), filter2) -> c(APP(app(encArg(x0), encArg(x1)), filter2))
   ENCODE_APP(cons_app(x0, x1), true) -> c(APP(app(encArg(x0), encArg(x1)), true))
   ENCODE_APP(cons_app(x0, x1), false) -> c(APP(app(encArg(x0), encArg(x1)), false))
   ENCODE_APP(cons_app(x0, x1), cons_app(z0, z1)) -> c(APP(app(encArg(x0), encArg(x1)), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(x0, \), x2) -> c(APP(app(encArg(x0), \), encArg(x2)))
   ENCODE_APP(cons_app(x0, e), x2) -> c(APP(app(encArg(x0), e), encArg(x2)))
   ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2)))
   ENCODE_APP(cons_app(x0, /), x2) -> c(APP(app(encArg(x0), /), encArg(x2)))
   ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(\, x1), x2) -> c(APP(app(\, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(e, x1), x2) -> c(APP(app(e, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(/, x1), x2) -> c(APP(app(/, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter2, x1), x2) -> c(APP(app(filter2, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(x0, cons_app(x1, \)) -> c(APP(encArg(x0), app(encArg(x1), \)))
   ENCODE_APP(x0, cons_app(x1, e)) -> c(APP(encArg(x0), app(encArg(x1), e)))
   ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .)))
   ENCODE_APP(x0, cons_app(x1, /)) -> c(APP(encArg(x0), app(encArg(x1), /)))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(\, x2)) -> c(APP(encArg(x0), app(\, encArg(x2))))
   ENCODE_APP(x0, cons_app(e, x2)) -> c(APP(encArg(x0), app(e, encArg(x2))))
   ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2))))
   ENCODE_APP(x0, cons_app(/, x2)) -> c(APP(encArg(x0), app(/, encArg(x2))))
   ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, \), x2) -> c(APP(app(encArg(x0), \), encArg(x2)))
   ENCODE_APP(cons_app(x0, e), x2) -> c(APP(app(encArg(x0), e), encArg(x2)))
   ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2)))
   ENCODE_APP(cons_app(x0, /), x2) -> c(APP(app(encArg(x0), /), encArg(x2)))
   ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(\, x1), x2) -> c(APP(app(\, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(e, x1), x2) -> c(APP(app(e, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(/, x1), x2) -> c(APP(app(/, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter2, x1), x2) -> c(APP(app(filter2, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c11_3, c11_2, c_1


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

(149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(cons_app(e, x1), x2) -> c(APP(app(e, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter2, x1), x2) -> c(APP(app(filter2, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2)))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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(\, z0), z0) -> e
   app(app(\, e), z0) -> z0
   app(app(\, z0), app(app(., z0), z1)) -> z1
   app(app(\, app(app(/, z0), z1)), z0) -> z1
   app(app(/, z0), z0) -> e
   app(app(/, z0), e) -> z0
   app(app(/, app(app(., z0), z1)), z1) -> z0
   app(app(/, z0), app(app(\, z1), z0)) -> z1
   app(app(., e), z0) -> z0
   app(app(., z0), e) -> z0
   app(app(., z0), app(app(\, z0), z1)) -> z1
   app(app(., app(app(/, z0), z1)), z1) -> z0
   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(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   ENCARG(cons_app(\, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(e, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(., x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(/, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c11(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c11(ENCARG(x1))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCARG(cons_app(x0, cons_app(x1, \))) -> c11(APP(encArg(x0), app(encArg(x1), \)), ENCARG(x0), ENCARG(cons_app(x1, \)))
   ENCARG(cons_app(x0, cons_app(x1, e))) -> c11(APP(encArg(x0), app(encArg(x1), e)), ENCARG(x0), ENCARG(cons_app(x1, e)))
   ENCARG(cons_app(x0, cons_app(x1, .))) -> c11(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .)))
   ENCARG(cons_app(x0, cons_app(x1, /))) -> c11(APP(encArg(x0), app(encArg(x1), /)), ENCARG(x0), ENCARG(cons_app(x1, /)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c11(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c11(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c11(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c11(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c11(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c11(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c11(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)))) -> c11(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(\, x2))) -> c11(APP(encArg(x0), app(\, encArg(x2))), ENCARG(x0), ENCARG(cons_app(\, x2)))
   ENCARG(cons_app(x0, cons_app(e, x2))) -> c11(APP(encArg(x0), app(e, encArg(x2))), ENCARG(x0), ENCARG(cons_app(e, x2)))
   ENCARG(cons_app(x0, cons_app(., x2))) -> c11(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2)))
   ENCARG(cons_app(x0, cons_app(/, x2))) -> c11(APP(encArg(x0), app(/, encArg(x2))), ENCARG(x0), ENCARG(cons_app(/, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c11(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c11(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c11(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c11(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c11(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c11(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c11(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))) -> c11(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))) -> c11(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(\, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(e, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(., cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(/, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c11(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, \), x2)) -> c11(APP(app(encArg(x0), \), encArg(x2)), ENCARG(cons_app(x0, \)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, e), x2)) -> c11(APP(app(encArg(x0), e), encArg(x2)), ENCARG(cons_app(x0, e)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, .), x2)) -> c11(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, /), x2)) -> c11(APP(app(encArg(x0), /), encArg(x2)), ENCARG(cons_app(x0, /)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c11(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c11(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c11(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c11(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c11(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c11(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c11(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)) -> c11(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(\, x1), x2)) -> c11(APP(app(\, encArg(x1)), encArg(x2)), ENCARG(cons_app(\, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(., x1), x2)) -> c11(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(/, x1), x2)) -> c11(APP(app(/, encArg(x1)), encArg(x2)), ENCARG(cons_app(/, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c11(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c11(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)) -> c11(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), \)) -> c11(APP(app(encArg(x0), encArg(x1)), \), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), e)) -> c11(APP(app(encArg(x0), encArg(x1)), e), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), .)) -> c11(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), /)) -> c11(APP(app(encArg(x0), encArg(x1)), /), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c11(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c11(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c11(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c11(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c11(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c11(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c11(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(e, x1), x2)) -> c11(ENCARG(cons_app(e, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c11(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c11(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c11(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c11(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c11(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), \) -> c(APP(app(encArg(z0), encArg(z1)), \))
   ENCODE_APP(cons_app(z0, z1), e) -> c(APP(app(encArg(z0), encArg(z1)), e))
   ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .))
   ENCODE_APP(cons_app(z0, z1), /) -> c(APP(app(encArg(z0), encArg(z1)), /))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(x0, cons_app(x1, \)) -> c(APP(encArg(x0), app(encArg(x1), \)))
   ENCODE_APP(x0, cons_app(x1, e)) -> c(APP(encArg(x0), app(encArg(x1), e)))
   ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .)))
   ENCODE_APP(x0, cons_app(x1, /)) -> c(APP(encArg(x0), app(encArg(x1), /)))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(\, x2)) -> c(APP(encArg(x0), app(\, encArg(x2))))
   ENCODE_APP(x0, cons_app(e, x2)) -> c(APP(encArg(x0), app(e, encArg(x2))))
   ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2))))
   ENCODE_APP(x0, cons_app(/, x2)) -> c(APP(encArg(x0), app(/, encArg(x2))))
   ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, \), x2) -> c(APP(app(encArg(x0), \), encArg(x2)))
   ENCODE_APP(cons_app(x0, e), x2) -> c(APP(app(encArg(x0), e), encArg(x2)))
   ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2)))
   ENCODE_APP(cons_app(x0, /), x2) -> c(APP(app(encArg(x0), /), encArg(x2)))
   ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(\, x1), x2) -> c(APP(app(\, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(/, x1), x2) -> c(APP(app(/, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   APP(app(\, z0), z0) -> c24
   APP(app(\, e), z0) -> c25
   APP(app(\, z0), app(app(., z0), z1)) -> c26
   APP(app(\, app(app(/, z0), z1)), z0) -> c27
   APP(app(/, z0), z0) -> c28
   APP(app(/, z0), e) -> c29
   APP(app(/, app(app(., z0), z1)), z1) -> c30
   APP(app(/, z0), app(app(\, z1), z0)) -> c31
   APP(app(., e), z0) -> c32
   APP(app(., z0), e) -> c33
   APP(app(., z0), app(app(\, z0), z1)) -> c34
   APP(app(., app(app(/, z0), z1)), z1) -> c35
   APP(app(map, z0), nil) -> c36
   APP(app(filter, z0), nil) -> c38
   APP(app(map, z0), app(app(cons, z1), z2)) -> c37(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c40(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c41(APP(app(filter, z0), z2))
   APP(app(filter, app(\, e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(\, e)), z0), x2), APP(app(\, e), z0))
   APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2), APP(app(\, z0), app(app(., z0), z1)))
   APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2), APP(app(\, app(app(/, z0), z1)), z0))
   APP(app(filter, app(/, z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, z0)), e), x2), APP(app(/, z0), e))
   APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2), APP(app(/, app(app(., z0), z1)), z1))
   APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)) -> c39(APP(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2), APP(app(/, z0), app(app(\, z1), z0)))
   APP(app(filter, app(., e)), app(app(cons, z0), x2)) -> c39(APP(app(app(app(filter2, z0), app(., e)), z0), x2), APP(app(., e), z0))
   APP(app(filter, app(., z0)), app(app(cons, e), x2)) -> c39(APP(app(app(app(filter2, z0), app(., z0)), e), x2), APP(app(., z0), e))
   APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)) -> c39(APP(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2), APP(app(., z0), app(app(\, z0), z1)))
   APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)) -> c39(APP(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2), APP(app(., app(app(/, z0), z1)), z1))
   APP(app(filter, app(\, z0)), app(app(cons, z0), x2)) -> c39(APP(app(\, z0), z0))
   APP(app(filter, app(/, z0)), app(app(cons, z0), x2)) -> c39(APP(app(/, z0), z0))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c39(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c39(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c39(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c39(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c39(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(\, e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(\, e)), z0), x2)), app(filter, app(\, e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, z0)), app(app(., z0), z1)), x2)), app(filter, app(\, z0))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(\, z0)), app(app(cons, app(app(., z0), z1)), x2)))
   APP(app(filter, app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(\, app(app(/, z0), z1))), z0), x2)), app(filter, app(\, app(app(/, z0), z1)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(\, app(app(/, z0), z1))), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, z0)), e), x2)), app(filter, app(/, z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(/, app(app(., z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(/, app(app(., z0), z1))), z1), x2)), app(filter, app(/, app(app(., z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(/, app(app(., z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, app(app(\, z1), z0)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(/, z0)), app(app(\, z1), z0)), x2)), app(filter, app(/, z0))), app(app(cons, app(app(\, z1), z0)), x2)), x3), APP(app(filter, app(/, z0)), app(app(cons, app(app(\, z1), z0)), x2)))
   APP(app(filter, app(filter, app(., e))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., e)), z0), x2)), app(filter, app(., e))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., e)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, e), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), e), x2)), app(filter, app(., z0))), app(app(cons, e), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, e), x2)))
   APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(\, z0), z1)), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(\, z0), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(\, z0), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(\, z0), z1)), x2)))
   APP(app(filter, app(filter, app(., app(app(/, z0), z1)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c39(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., app(app(/, z0), z1))), z1), x2)), app(filter, app(., app(app(/, z0), z1)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(., app(app(/, z0), z1))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c39(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)) -> c39(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(\, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(\, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(/, z0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c39(APP(app(filter, app(/, z0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(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)) -> c39(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c39(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:   c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c37_2, c40_1, c41_1, c11_1, c39_2, c39_1, c11_3, c11_2, c_1


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

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

(152)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(c_app(\, e), x) -> x
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
   app(c_app(/, x), c_app(c_app(\, y), x)) -> y
   app(c_app(., c_app(c_app(/, y), x)), x) -> y
   app(c_app(map, f), nil) -> nil
   app(c_app(filter, f), nil) -> nil
   app(c_app(\, c_app(c_app(/, x), y)), x) -> y
   app(c_app(\, x), x) -> e
   app(c_app(\, x), c_app(c_app(., x), y)) -> y
   app(c_app(., e), x) -> x
   app(c_app(/, x), e) -> x
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(c_app(., x), e) -> x
   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(/, x), x) -> e
   app(c_app(/, c_app(c_app(., y), x)), x) -> y
   app(c_app(., x), c_app(c_app(\, x), y)) -> y

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

   encArg(\) -> \
   encArg(e) -> e
   encArg(.) -> .
   encArg(/) -> /
   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_\ -> \
   encode_e -> e
   encode_. -> .
   encode_/ -> /
   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
----------------------------------------

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

(154)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(\, e), x) -> x [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(/, x), c_app(c_app(\, y), x)) -> y [1]
   app(c_app(., c_app(c_app(/, y), x)), x) -> y [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(\, c_app(c_app(/, x), y)), x) -> y [1]
   app(c_app(\, x), x) -> e [1]
   app(c_app(\, x), c_app(c_app(., x), y)) -> y [1]
   app(c_app(., e), x) -> x [1]
   app(c_app(/, x), e) -> x [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(., x), e) -> x [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(/, x), x) -> e [1]
   app(c_app(/, c_app(c_app(., y), x)), x) -> y [1]
   app(c_app(., x), c_app(c_app(\, x), y)) -> y [1]
   encArg(\) -> \ [0]
   encArg(e) -> e [0]
   encArg(.) -> . [0]
   encArg(/) -> / [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_\ -> \ [0]
   encode_e -> e [0]
   encode_. -> . [0]
   encode_/ -> / [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
----------------------------------------

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

(156)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(\, e), x) -> x [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(/, x), c_app(c_app(\, y), x)) -> y [1]
   app(c_app(., c_app(c_app(/, y), x)), x) -> y [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(\, c_app(c_app(/, x), y)), x) -> y [1]
   app(c_app(\, x), x) -> e [1]
   app(c_app(\, x), c_app(c_app(., x), y)) -> y [1]
   app(c_app(., e), x) -> x [1]
   app(c_app(/, x), e) -> x [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(., x), e) -> x [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(/, x), x) -> e [1]
   app(c_app(/, c_app(c_app(., y), x)), x) -> y [1]
   app(c_app(., x), c_app(c_app(\, x), y)) -> y [1]
   encArg(\) -> \ [0]
   encArg(e) -> e [0]
   encArg(.) -> . [0]
   encArg(/) -> / [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_\ -> \ [0]
   encode_e -> e [0]
   encode_. -> . [0]
   encode_/ -> / [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [0]
   app(x0, x1) -> c_app(x0, x1) [0]

The TRS has the following type information:
app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
c_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
\ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
/ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
. :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
cons_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_\ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_. :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_/ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app
encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app

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

(157) 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_\
   encode_e
   encode_.
   encode_/
   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_\ -> null_encode_\ [0]
   encode_e -> null_encode_e [0]
   encode_. -> null_encode_. [0]
   encode_/ -> null_encode_/ [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_\, null_encode_e, null_encode_., null_encode_/, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app

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

(158)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(\, e), x) -> x [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(/, x), c_app(c_app(\, y), x)) -> y [1]
   app(c_app(., c_app(c_app(/, y), x)), x) -> y [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(\, c_app(c_app(/, x), y)), x) -> y [1]
   app(c_app(\, x), x) -> e [1]
   app(c_app(\, x), c_app(c_app(., x), y)) -> y [1]
   app(c_app(., e), x) -> x [1]
   app(c_app(/, x), e) -> x [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(., x), e) -> x [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(/, x), x) -> e [1]
   app(c_app(/, c_app(c_app(., y), x)), x) -> y [1]
   app(c_app(., x), c_app(c_app(\, x), y)) -> y [1]
   encArg(\) -> \ [0]
   encArg(e) -> e [0]
   encArg(.) -> . [0]
   encArg(/) -> / [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_\ -> \ [0]
   encode_e -> e [0]
   encode_. -> . [0]
   encode_/ -> / [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_\ -> null_encode_\ [0]
   encode_e -> null_encode_e [0]
   encode_. -> null_encode_. [0]
   encode_/ -> null_encode_/ [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
c_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
\ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
/ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
. :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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
----------------------------------------

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

(160)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(\, e), x) -> x [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(/, x), c_app(c_app(\, y), x)) -> y [1]
   app(c_app(., c_app(c_app(/, y), x)), x) -> y [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(\, c_app(c_app(/, x), y)), x) -> y [1]
   app(c_app(\, x), x) -> e [1]
   app(c_app(\, x), c_app(c_app(., x), y)) -> y [1]
   app(c_app(., e), x) -> x [1]
   app(c_app(/, x), e) -> x [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(., x), e) -> x [1]
   app(c_app(filter, c_app(map, f5)), c_app(c_app(cons, c_app(c_app(cons, x9), xs1)), xs)) -> app(app(app(app(filter2, app(app(cons, app(f5, x9)), app(app(map, f5), xs1))), c_app(map, f5)), c_app(c_app(cons, x9), xs1)), xs) [2]
   app(c_app(filter, c_app(\, e)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, x), c_app(\, e)), x), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, false), f6), x10)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(filter, f6), x)), c_app(c_app(c_app(filter2, false), f6), x10)), x), xs) [2]
   app(c_app(filter, c_app(/, x11)), c_app(c_app(cons, c_app(c_app(\, y5), x11)), xs)) -> app(app(app(app(filter2, y5), c_app(/, x11)), c_app(c_app(\, y5), x11)), xs) [2]
   app(c_app(filter, c_app(., c_app(c_app(/, y6), x))), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, y6), c_app(., c_app(c_app(/, y6), x))), x), xs) [2]
   app(c_app(filter, c_app(map, f7)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(map, f7)), nil), xs) [2]
   app(c_app(filter, c_app(filter, f8)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(filter, f8)), nil), xs) [2]
   app(c_app(filter, c_app(\, c_app(c_app(/, x), y7))), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, y7), c_app(\, c_app(c_app(/, x), y7))), x), xs) [2]
   app(c_app(filter, c_app(\, x)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, e), c_app(\, x)), x), xs) [2]
   app(c_app(filter, c_app(\, x12)), c_app(c_app(cons, c_app(c_app(., x12), y8)), xs)) -> app(app(app(app(filter2, y8), c_app(\, x12)), c_app(c_app(., x12), y8)), xs) [2]
   app(c_app(filter, c_app(., e)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, x), c_app(., e)), x), xs) [2]
   app(c_app(filter, c_app(/, x13)), c_app(c_app(cons, e), xs)) -> app(app(app(app(filter2, x13), c_app(/, x13)), e), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, true), f9), x14)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(cons, x14), app(app(filter, f9), x))), c_app(c_app(c_app(filter2, true), f9), x14)), x), xs) [2]
   app(c_app(filter, c_app(., x15)), c_app(c_app(cons, e), xs)) -> app(app(app(app(filter2, x15), c_app(., x15)), e), xs) [2]
   app(c_app(filter, c_app(filter, f10)), c_app(c_app(cons, c_app(c_app(cons, x16), xs2)), xs)) -> app(app(app(app(filter2, app(app(app(app(filter2, app(f10, x16)), f10), x16), xs2)), c_app(filter, f10)), c_app(c_app(cons, x16), xs2)), xs) [2]
   app(c_app(filter, c_app(/, x)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, e), c_app(/, x)), x), xs) [2]
   app(c_app(filter, c_app(/, c_app(c_app(., y9), x))), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, y9), c_app(/, c_app(c_app(., y9), x))), x), xs) [2]
   app(c_app(filter, c_app(., x17)), c_app(c_app(cons, c_app(c_app(\, x17), y10)), xs)) -> app(app(app(app(filter2, y10), c_app(., x17)), c_app(c_app(\, x17), y10)), 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(/, x), x) -> e [1]
   app(c_app(/, c_app(c_app(., y), x)), x) -> y [1]
   app(c_app(., x), c_app(c_app(\, x), y)) -> y [1]
   encArg(\) -> \ [0]
   encArg(e) -> e [0]
   encArg(.) -> . [0]
   encArg(/) -> / [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_\ -> \ [0]
   encode_e -> e [0]
   encode_. -> . [0]
   encode_/ -> / [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_\ -> null_encode_\ [0]
   encode_e -> null_encode_e [0]
   encode_. -> null_encode_. [0]
   encode_/ -> null_encode_/ [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
c_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
\ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
/ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
. :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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
----------------------------------------

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

   map => 8
   cons => 3
   \ => 2
   e => 4
   filter2 => 7
   false => 5
   filter => 6
   / => 1
   . => 0
   nil => 9
   true => 10
   null_encArg => 0
   null_encode_app => 0
   null_encode_\ => 0
   null_encode_e => 0
   null_encode_. => 0
   null_encode_/ => 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

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

(162)
Obligation:
Complexity RNTS consisting of the following rules:

   app(z, z') -{ 1 }-> x :|: z' = x, z = 1 + 2 + 4, x >= 0
   app(z, z') -{ 1 }-> x :|: z' = x, x >= 0, z = 1 + 0 + 4
   app(z, z') -{ 1 }-> x :|: z' = 4, x >= 0, z = 1 + 1 + x
   app(z, z') -{ 1 }-> x :|: z' = 4, x >= 0, z = 1 + 0 + x
   app(z, z') -{ 1 }-> y :|: z' = 1 + (1 + 2 + y) + x, x >= 0, y >= 0, z = 1 + 1 + x
   app(z, z') -{ 1 }-> y :|: z' = x, z = 1 + 0 + (1 + (1 + 1 + y) + x), y >= 0, x >= 0
   app(z, z') -{ 1 }-> y :|: z' = x, x >= 0, y >= 0, z = 1 + 2 + (1 + (1 + 1 + x) + y)
   app(z, z') -{ 1 }-> y :|: z' = 1 + (1 + 0 + x) + y, x >= 0, y >= 0, z = 1 + 2 + x
   app(z, z') -{ 1 }-> y :|: z = 1 + 1 + (1 + (1 + 0 + y) + x), z' = x, y >= 0, x >= 0
   app(z, z') -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + 0 + x, z' = 1 + (1 + 2 + x) + y
   app(z, z') -{ 2 }-> app(app(app(app(7, x), 1 + 2 + 4), x), xs) :|: xs >= 0, x >= 0, z = 1 + 6 + (1 + 2 + 4), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, x), 1 + 0 + 4), x), xs) :|: xs >= 0, z = 1 + 6 + (1 + 0 + 4), x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, x13), 1 + 1 + x13), 4), xs) :|: x13 >= 0, xs >= 0, z = 1 + 6 + (1 + 1 + x13), z' = 1 + (1 + 3 + 4) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, x15), 1 + 0 + x15), 4), xs) :|: xs >= 0, z = 1 + 6 + (1 + 0 + x15), z' = 1 + (1 + 3 + 4) + xs, x15 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, y10), 1 + 0 + x17), 1 + (1 + 2 + x17) + y10), xs) :|: xs >= 0, x17 >= 0, y10 >= 0, z = 1 + 6 + (1 + 0 + x17), z' = 1 + (1 + 3 + (1 + (1 + 2 + x17) + y10)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y5), 1 + 1 + x11), 1 + (1 + 2 + y5) + x11), xs) :|: y5 >= 0, xs >= 0, z' = 1 + (1 + 3 + (1 + (1 + 2 + y5) + x11)) + xs, x11 >= 0, z = 1 + 6 + (1 + 1 + x11)
   app(z, z') -{ 2 }-> app(app(app(app(7, y6), 1 + 0 + (1 + (1 + 1 + y6) + x)), x), xs) :|: xs >= 0, x >= 0, y6 >= 0, z = 1 + 6 + (1 + 0 + (1 + (1 + 1 + y6) + x)), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y7), 1 + 2 + (1 + (1 + 1 + x) + y7)), x), xs) :|: xs >= 0, x >= 0, y7 >= 0, z = 1 + 6 + (1 + 2 + (1 + (1 + 1 + x) + y7)), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y8), 1 + 2 + x12), 1 + (1 + 0 + x12) + y8), xs) :|: xs >= 0, y8 >= 0, x12 >= 0, z = 1 + 6 + (1 + 2 + x12), z' = 1 + (1 + 3 + (1 + (1 + 0 + x12) + y8)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y9), 1 + 1 + (1 + (1 + 0 + y9) + x)), x), xs) :|: y9 >= 0, xs >= 0, z = 1 + 6 + (1 + 1 + (1 + (1 + 0 + y9) + x)), x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(app(app(7, app(f10, x16)), f10), x16), xs2)), 1 + 6 + f10), 1 + (1 + 3 + x16) + xs2), xs) :|: z' = 1 + (1 + 3 + (1 + (1 + 3 + x16) + xs2)) + xs, xs >= 0, xs2 >= 0, f10 >= 0, z = 1 + 6 + (1 + 6 + f10), x16 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(6, f6), x)), 1 + (1 + (1 + 7 + 5) + f6) + x10), x), xs) :|: xs >= 0, x >= 0, f6 >= 0, x10 >= 0, z = 1 + 6 + (1 + (1 + (1 + 7 + 5) + f6) + x10), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(3, x14), app(app(6, f9), x))), 1 + (1 + (1 + 7 + 10) + f9) + x14), x), xs) :|: xs >= 0, x >= 0, x14 >= 0, f9 >= 0, z = 1 + 6 + (1 + (1 + (1 + 7 + 10) + f9) + x14), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(3, app(f5, x9)), app(app(8, f5), xs1))), 1 + 8 + f5), 1 + (1 + 3 + x9) + xs1), xs) :|: xs >= 0, z = 1 + 6 + (1 + 8 + f5), xs1 >= 0, f5 >= 0, z' = 1 + (1 + 3 + (1 + (1 + 3 + x9) + xs1)) + xs, x9 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, 9), 1 + 8 + f7), 9), xs) :|: z = 1 + 6 + (1 + 8 + f7), xs >= 0, z' = 1 + (1 + 3 + 9) + xs, f7 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, 9), 1 + 6 + f8), 9), xs) :|: f8 >= 0, xs >= 0, z' = 1 + (1 + 3 + 9) + xs, z = 1 + 6 + (1 + 6 + f8)
   app(z, z') -{ 2 }-> app(app(app(app(7, 4), 1 + 2 + x), x), xs) :|: xs >= 0, x >= 0, z = 1 + 6 + (1 + 2 + x), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, 4), 1 + 1 + x), x), xs) :|: xs >= 0, x >= 0, z = 1 + 6 + (1 + 1 + x), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(app(7, 0), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(app(7, 1 + f + x), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(app(3, app(f, x)), app(app(8, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 8 + f, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(0, xs) :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(0, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x, z' = xs
   app(z, z') -{ 1 }-> app(0, app(1 + 6 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x, z' = xs
   app(z, z') -{ 1 }-> app(1 + 6 + f, xs) :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(1 + 3 + x, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x, z' = xs
   app(z, z') -{ 1 }-> app(1 + 3 + x, app(1 + 6 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x, z' = xs
   app(z, z') -{ 1 }-> 9 :|: f >= 0, z = 1 + 8 + f, z' = 9
   app(z, z') -{ 1 }-> 9 :|: f >= 0, z = 1 + 6 + f, z' = 9
   app(z, z') -{ 1 }-> 4 :|: z' = x, x >= 0, z = 1 + 2 + x
   app(z, z') -{ 1 }-> 4 :|: z' = x, x >= 0, z = 1 + 1 + x
   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 }-> 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 :|: 
   encode_/ -{ 0 }-> 1 :|: 
   encode_/ -{ 0 }-> 0 :|: 
   encode_\ -{ 0 }-> 2 :|: 
   encode_\ -{ 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 }-> 3 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_e -{ 0 }-> 4 :|: 
   encode_e -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 5 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 6 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 7 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 8 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 9 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 10 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

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

(164)
Obligation:
Complexity RNTS consisting of the following rules:

   app(z, z') -{ 1 }-> y :|: z' = 1 + (1 + 2 + y) + (z - 2), z - 2 >= 0, y >= 0
   app(z, z') -{ 1 }-> y :|: z = 1 + 0 + (1 + (1 + 1 + y) + z'), y >= 0, z' >= 0
   app(z, z') -{ 1 }-> y :|: z' >= 0, y >= 0, z = 1 + 2 + (1 + (1 + 1 + z') + y)
   app(z, z') -{ 1 }-> y :|: z' = 1 + (1 + 0 + (z - 3)) + y, z - 3 >= 0, y >= 0
   app(z, z') -{ 1 }-> y :|: z = 1 + 1 + (1 + (1 + 0 + y) + z'), y >= 0, z' >= 0
   app(z, z') -{ 1 }-> y :|: z - 1 >= 0, y >= 0, z' = 1 + (1 + 2 + (z - 1)) + y
   app(z, z') -{ 1 }-> z' :|: z = 1 + 2 + 4, z' >= 0
   app(z, z') -{ 1 }-> z' :|: z' >= 0, z = 1 + 0 + 4
   app(z, z') -{ 2 }-> app(app(app(app(7, x), 1 + 2 + 4), x), xs) :|: xs >= 0, x >= 0, z = 1 + 6 + (1 + 2 + 4), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, x), 1 + 0 + 4), x), xs) :|: xs >= 0, z = 1 + 6 + (1 + 0 + 4), x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y10), 1 + 0 + (z - 8)), 1 + (1 + 2 + (z - 8)) + y10), xs) :|: xs >= 0, z - 8 >= 0, y10 >= 0, z' = 1 + (1 + 3 + (1 + (1 + 2 + (z - 8)) + y10)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y5), 1 + 1 + (z - 9)), 1 + (1 + 2 + y5) + (z - 9)), xs) :|: y5 >= 0, xs >= 0, z' = 1 + (1 + 3 + (1 + (1 + 2 + y5) + (z - 9))) + xs, z - 9 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, y6), 1 + 0 + (1 + (1 + 1 + y6) + x)), x), xs) :|: xs >= 0, x >= 0, y6 >= 0, z = 1 + 6 + (1 + 0 + (1 + (1 + 1 + y6) + x)), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y7), 1 + 2 + (1 + (1 + 1 + x) + y7)), x), xs) :|: xs >= 0, x >= 0, y7 >= 0, z = 1 + 6 + (1 + 2 + (1 + (1 + 1 + x) + y7)), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y8), 1 + 2 + (z - 10)), 1 + (1 + 0 + (z - 10)) + y8), xs) :|: xs >= 0, y8 >= 0, z - 10 >= 0, z' = 1 + (1 + 3 + (1 + (1 + 0 + (z - 10)) + y8)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, y9), 1 + 1 + (1 + (1 + 0 + y9) + x)), x), xs) :|: y9 >= 0, xs >= 0, z = 1 + 6 + (1 + 1 + (1 + (1 + 0 + y9) + x)), x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(app(app(7, app(z - 14, x16)), z - 14), x16), xs2)), 1 + 6 + (z - 14)), 1 + (1 + 3 + x16) + xs2), xs) :|: z' = 1 + (1 + 3 + (1 + (1 + 3 + x16) + xs2)) + xs, xs >= 0, xs2 >= 0, z - 14 >= 0, x16 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(6, f6), x)), 1 + (1 + (1 + 7 + 5) + f6) + x10), x), xs) :|: xs >= 0, x >= 0, f6 >= 0, x10 >= 0, z = 1 + 6 + (1 + (1 + (1 + 7 + 5) + f6) + x10), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(3, x14), app(app(6, f9), x))), 1 + (1 + (1 + 7 + 10) + f9) + x14), x), xs) :|: xs >= 0, x >= 0, x14 >= 0, f9 >= 0, z = 1 + 6 + (1 + (1 + (1 + 7 + 10) + f9) + x14), z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, app(app(3, app(z - 16, x9)), app(app(8, z - 16), xs1))), 1 + 8 + (z - 16)), 1 + (1 + 3 + x9) + xs1), xs) :|: xs >= 0, xs1 >= 0, z - 16 >= 0, z' = 1 + (1 + 3 + (1 + (1 + 3 + x9) + xs1)) + xs, x9 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, 9), 1 + 8 + (z - 16)), 9), z' - 14) :|: z' - 14 >= 0, z - 16 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, 9), 1 + 6 + (z - 14)), 9), z' - 14) :|: z - 14 >= 0, z' - 14 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, 4), 1 + 2 + (z - 10)), z - 10), xs) :|: xs >= 0, z - 10 >= 0, z' = 1 + (1 + 3 + (z - 10)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, 4), 1 + 1 + (z - 9)), z - 9), xs) :|: xs >= 0, z - 9 >= 0, z' = 1 + (1 + 3 + (z - 9)) + xs
   app(z, z') -{ 1 }-> app(app(app(app(7, 0), z - 7), x), xs) :|: z - 7 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(7, z - 9), 1 + 1 + (z - 9)), 4), z' - 9) :|: z - 9 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(7, z - 8), 1 + 0 + (z - 8)), 4), z' - 9) :|: z' - 9 >= 0, z - 8 >= 0
   app(z, z') -{ 1 }-> app(app(app(app(7, 1 + (z - 7) + x), z - 7), x), xs) :|: z - 7 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(app(3, app(z - 9, x)), app(app(8, z - 9), xs)) :|: z - 9 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(0, z') :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, z' >= 0, x >= 0
   app(z, z') -{ 1 }-> app(0, app(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x
   app(z, z') -{ 1 }-> app(0, app(1 + 6 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x
   app(z, z') -{ 1 }-> app(1 + 6 + f, z') :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, z' >= 0, x >= 0
   app(z, z') -{ 1 }-> app(1 + 3 + x, app(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x
   app(z, z') -{ 1 }-> app(1 + 3 + x, app(1 + 6 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x
   app(z, z') -{ 1 }-> 9 :|: z - 9 >= 0, z' = 9
   app(z, z') -{ 1 }-> 9 :|: z - 7 >= 0, z' = 9
   app(z, z') -{ 1 }-> 4 :|: z' >= 0, z = 1 + 2 + z'
   app(z, z') -{ 1 }-> 4 :|: z' >= 0, z = 1 + 1 + z'
   app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   app(z, z') -{ 1 }-> z - 2 :|: z' = 4, z - 2 >= 0
   app(z, z') -{ 1 }-> z - 1 :|: z' = 4, z - 1 >= 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 }-> 10 :|: z = 10
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_. -{ 0 }-> 0 :|: 
   encode_/ -{ 0 }-> 1 :|: 
   encode_/ -{ 0 }-> 0 :|: 
   encode_\ -{ 0 }-> 2 :|: 
   encode_\ -{ 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 }-> 3 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_e -{ 0 }-> 4 :|: 
   encode_e -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 5 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 6 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 7 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 8 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 9 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 10 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

(165) 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_\ -> null_encode_\ [0]
   encode_e -> null_encode_e [0]
   encode_. -> null_encode_. [0]
   encode_/ -> null_encode_/ [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_\, null_encode_e, null_encode_., null_encode_/, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app

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

(166)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(\, e), x) -> x [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(/, x), c_app(c_app(\, y), x)) -> y [1]
   app(c_app(., c_app(c_app(/, y), x)), x) -> y [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(\, c_app(c_app(/, x), y)), x) -> y [1]
   app(c_app(\, x), x) -> e [1]
   app(c_app(\, x), c_app(c_app(., x), y)) -> y [1]
   app(c_app(., e), x) -> x [1]
   app(c_app(/, x), e) -> x [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(., x), e) -> x [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(/, x), x) -> e [1]
   app(c_app(/, c_app(c_app(., y), x)), x) -> y [1]
   app(c_app(., x), c_app(c_app(\, x), y)) -> y [1]
   encArg(\) -> \ [0]
   encArg(e) -> e [0]
   encArg(.) -> . [0]
   encArg(/) -> / [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_\ -> \ [0]
   encode_e -> e [0]
   encode_. -> . [0]
   encode_/ -> / [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_\ -> null_encode_\ [0]
   encode_e -> null_encode_e [0]
   encode_. -> null_encode_. [0]
   encode_/ -> null_encode_/ [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
c_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
\ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
/ :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
. :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encArg :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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_e :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_map :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_nil :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_cons :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter2 :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_true :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_false :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_app :: map:c_app:cons:\:e:filter2:false:filter:/:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_\:null_encode_e:null_encode_.:null_encode_/: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
----------------------------------------

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

   map => 8
   cons => 3
   \ => 2
   e => 4
   filter2 => 7
   false => 5
   filter => 6
   / => 1
   . => 0
   nil => 9
   true => 10
   null_encArg => 0
   null_encode_app => 0
   null_encode_\ => 0
   null_encode_e => 0
   null_encode_. => 0
   null_encode_/ => 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

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

(168)
Obligation:
Complexity RNTS consisting of the following rules:

   app(z, z') -{ 1 }-> x :|: z' = x, z = 1 + 2 + 4, x >= 0
   app(z, z') -{ 1 }-> x :|: z' = x, x >= 0, z = 1 + 0 + 4
   app(z, z') -{ 1 }-> x :|: z' = 4, x >= 0, z = 1 + 1 + x
   app(z, z') -{ 1 }-> x :|: z' = 4, x >= 0, z = 1 + 0 + x
   app(z, z') -{ 1 }-> y :|: z' = 1 + (1 + 2 + y) + x, x >= 0, y >= 0, z = 1 + 1 + x
   app(z, z') -{ 1 }-> y :|: z' = x, z = 1 + 0 + (1 + (1 + 1 + y) + x), y >= 0, x >= 0
   app(z, z') -{ 1 }-> y :|: z' = x, x >= 0, y >= 0, z = 1 + 2 + (1 + (1 + 1 + x) + y)
   app(z, z') -{ 1 }-> y :|: z' = 1 + (1 + 0 + x) + y, x >= 0, y >= 0, z = 1 + 2 + x
   app(z, z') -{ 1 }-> y :|: z = 1 + 1 + (1 + (1 + 0 + y) + x), z' = x, y >= 0, x >= 0
   app(z, z') -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + 0 + x, z' = 1 + (1 + 2 + x) + y
   app(z, z') -{ 1 }-> app(app(app(app(7, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> app(app(6, f), xs) :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(app(3, x), app(app(6, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 10) + f) + x, z' = xs
   app(z, z') -{ 1 }-> app(app(3, app(f, x)), app(app(8, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 8 + f, z' = 1 + (1 + 3 + x) + xs
   app(z, z') -{ 1 }-> 9 :|: f >= 0, z = 1 + 8 + f, z' = 9
   app(z, z') -{ 1 }-> 9 :|: f >= 0, z = 1 + 6 + f, z' = 9
   app(z, z') -{ 1 }-> 4 :|: z' = x, x >= 0, z = 1 + 2 + x
   app(z, z') -{ 1 }-> 4 :|: z' = x, x >= 0, z = 1 + 1 + x
   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 }-> 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 :|: 
   encode_/ -{ 0 }-> 1 :|: 
   encode_/ -{ 0 }-> 0 :|: 
   encode_\ -{ 0 }-> 2 :|: 
   encode_\ -{ 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 }-> 3 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_e -{ 0 }-> 4 :|: 
   encode_e -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 5 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 6 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 7 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 8 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 9 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 10 :|: 
   encode_true -{ 0 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.