KILLED
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 194 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 9 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 14.4 s]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 2 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 2 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(36) CdtProblem
    (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms]
    (64) CdtProblem
    (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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), 0 ms]
    (92) CdtProblem
    (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (96) CdtProblem
    (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 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), 17 ms]
    (112) CdtProblem
    (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
    (124) CdtProblem
    (125) CdtRhsSimplificationProcessorProof [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), 8 ms]
    (136) CdtProblem
    (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem


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

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


The TRS R consists of the following rules:

   app(g, app(h, app(g, x))) -> app(g, x)
   app(g, app(g, x)) -> app(g, app(h, app(g, x)))
   app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), 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(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   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(g, app(h, app(g, x))) -> app(g, x)
   app(g, app(g, x)) -> app(g, app(h, app(g, x)))
   app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)

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

   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   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(g, app(h, app(g, x))) -> app(g, x)
   app(g, app(g, x)) -> app(g, app(h, app(g, x)))
   app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)

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

   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   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(g, app(h, app(g, x))) -> app(g, x)
   app(g, app(g, x)) -> app(g, app(h, app(g, x)))
   app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)

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

   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   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(g, app(h, app(g, x))) -> app(g, x)
app(g, app(g, x)) -> app(g, app(h, app(g, x)))
app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
app(app(map, fun), nil) -> nil
app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
app(app(filter, fun), nil) -> nil
app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)
encArg(g) -> g
encArg(h) -> h
encArg(f) -> f
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_g -> g
encode_h -> h
encode_f -> f
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2
encode_true -> true
encode_false -> false

Types:
app :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
g :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
h :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
f :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
map :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
nil :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
cons :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
filter :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
true :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
false :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_g :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_h :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_f :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
hole_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app1_0 :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0 :: Nat -> g:h:f: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(g, app(h, app(g, x))) -> app(g, x)
app(g, app(g, x)) -> app(g, app(h, app(g, x)))
app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
app(app(map, fun), nil) -> nil
app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
app(app(filter, fun), nil) -> nil
app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)
encArg(g) -> g
encArg(h) -> h
encArg(f) -> f
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_g -> g
encode_h -> h
encode_f -> f
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2
encode_true -> true
encode_false -> false

Types:
app :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
g :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
h :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
f :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
map :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
nil :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
cons :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
filter :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
true :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
false :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_g :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_h :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_f :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
hole_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app1_0 :: g:h:f:map:nil:cons:filter:filter2:true:false:cons_app
gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0 :: Nat -> g:h:f:map:nil:cons:filter:filter2:true:false:cons_app


Generator Equations:
gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(0) <=> g
gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(+(x, 1)) <=> cons_app(g, gen_g:h:f: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) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(n5219_0)) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(0))

Induction Step:
encArg(gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(+(n5219_0, 1))) ->_R^Omega(0)
app(encArg(g), encArg(gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(n5219_0))) ->_R^Omega(0)
app(g, encArg(gen_g:h:f:map:nil:cons:filter:filter2:true:false:cons_app2_0(n5219_0))) ->_IH
app(g, *3_0)

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

(12)
BOUNDS(1, INF)

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

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

(14)
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(g, app(h, app(g, x))) -> app(g, x)
   app(g, app(g, x)) -> app(g, app(h, app(g, x)))
   app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)

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

   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

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


The TRS R consists of the following rules:

   app(g, app(h, app(g, x))) -> app(g, x)
   app(g, app(g, x)) -> app(g, app(h, app(g, x)))
   app(h, app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(18)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(g, c_app(h, c_app(g, x))) -> app(g, x)
   app(h, c_app(h, x)) -> app(h, app(app(f, app(h, x)), x))
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)
   app(g, c_app(g, x)) -> app(g, app(h, app(g, x)))
   app(c_app(map, fun), nil) -> nil
   app(c_app(filter, fun), nil) -> nil
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)

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

   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(x0, x1) -> c_app(x0, x1)

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

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

(20)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1]
   app(g, c_app(h, c_app(g, x))) -> app(g, x) [1]
   app(h, c_app(h, x)) -> app(h, app(app(f, app(h, x)), x)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1]
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1]
   app(g, c_app(g, x)) -> app(g, app(h, app(g, x))) [1]
   app(c_app(map, fun), nil) -> nil [1]
   app(c_app(filter, fun), nil) -> nil [1]
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1]
   encArg(g) -> g [0]
   encArg(h) -> h [0]
   encArg(f) -> f [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_g -> g [0]
   encode_h -> h [0]
   encode_f -> f [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [0]
   app(x0, x1) -> c_app(x0, x1) [0]

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

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

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

   app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1]
   app(g, c_app(h, c_app(g, x))) -> app(g, x) [1]
   app(h, c_app(h, x)) -> app(h, app(app(f, app(h, x)), x)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1]
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1]
   app(g, c_app(g, x)) -> app(g, app(h, app(g, x))) [1]
   app(c_app(map, fun), nil) -> nil [1]
   app(c_app(filter, fun), nil) -> nil [1]
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1]
   encArg(g) -> g [0]
   encArg(h) -> h [0]
   encArg(f) -> f [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_g -> g [0]
   encode_h -> h [0]
   encode_f -> f [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:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
c_app :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
map :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
cons :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
filter2 :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
true :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
filter :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
false :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
nil :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encArg :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
cons_app :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_app :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app -> map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_map :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_nil :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_cons :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_filter :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_filter2 :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_true :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app
encode_false :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app

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

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

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

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

(c) The following functions are completely defined:

   encArg_1
   encode_app_2
   encode_g
   encode_h
   encode_f
   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_g -> null_encode_g [0]
   encode_h -> null_encode_h [0]
   encode_f -> null_encode_f [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_g, null_encode_h, null_encode_f, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app

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

(24)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1]
   app(g, c_app(h, c_app(g, x))) -> app(g, x) [1]
   app(h, c_app(h, x)) -> app(h, app(app(f, app(h, x)), x)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1]
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1]
   app(g, c_app(g, x)) -> app(g, app(h, app(g, x))) [1]
   app(c_app(map, fun), nil) -> nil [1]
   app(c_app(filter, fun), nil) -> nil [1]
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1]
   encArg(g) -> g [0]
   encArg(h) -> h [0]
   encArg(f) -> f [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_g -> g [0]
   encode_h -> h [0]
   encode_f -> f [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_g -> null_encode_g [0]
   encode_h -> null_encode_h [0]
   encode_f -> null_encode_f [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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app

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

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

(26)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1]
   app(g, c_app(h, c_app(g, x))) -> app(g, x) [1]
   app(h, c_app(h, c_app(h, x7))) -> app(h, app(app(f, app(h, app(app(f, app(h, x7)), x7))), c_app(h, x7))) [2]
   app(h, c_app(h, x)) -> app(h, app(app(f, c_app(h, x)), x)) [1]
   app(h, c_app(h, x)) -> app(h, app(app(f, null_app), x)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(c_app(cons, x), app(c_app(filter, fun), xs)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(c_app(cons, x), app(null_app, xs)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(null_app, app(c_app(filter, fun), xs)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(null_app, app(null_app, xs)) [1]
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(c_app(filter, fun), xs) [1]
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(null_app, xs) [1]
   app(g, c_app(g, c_app(h, c_app(g, x8)))) -> app(g, app(h, app(g, x8))) [2]
   app(g, c_app(g, c_app(g, x9))) -> app(g, app(h, app(g, app(h, app(g, x9))))) [2]
   app(g, c_app(g, x)) -> app(g, app(h, c_app(g, x))) [1]
   app(g, c_app(g, x)) -> app(g, app(h, null_app)) [1]
   app(c_app(map, fun), nil) -> nil [1]
   app(c_app(filter, fun), nil) -> nil [1]
   app(c_app(filter, c_app(map, fun5)), c_app(c_app(cons, c_app(c_app(cons, x10), xs1)), xs)) -> app(app(app(app(filter2, app(app(cons, app(fun5, x10)), app(app(map, fun5), xs1))), c_app(map, fun5)), c_app(c_app(cons, x10), xs1)), xs) [2]
   app(c_app(filter, g), c_app(c_app(cons, c_app(h, c_app(g, x11))), xs)) -> app(app(app(app(filter2, app(g, x11)), g), c_app(h, c_app(g, x11))), xs) [2]
   app(c_app(filter, h), c_app(c_app(cons, c_app(h, x12)), xs)) -> app(app(app(app(filter2, app(h, app(app(f, app(h, x12)), x12))), h), c_app(h, x12)), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, true), fun6), x13)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(cons, x13), app(app(filter, fun6), x))), c_app(c_app(c_app(filter2, true), fun6), x13)), x), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, false), fun7), x14)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(filter, fun7), x)), c_app(c_app(c_app(filter2, false), fun7), x14)), x), xs) [2]
   app(c_app(filter, g), c_app(c_app(cons, c_app(g, x15)), xs)) -> app(app(app(app(filter2, app(g, app(h, app(g, x15)))), g), c_app(g, x15)), xs) [2]
   app(c_app(filter, c_app(map, fun8)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(map, fun8)), nil), xs) [2]
   app(c_app(filter, c_app(filter, fun9)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(filter, fun9)), nil), xs) [2]
   app(c_app(filter, c_app(filter, fun10)), c_app(c_app(cons, c_app(c_app(cons, x16), xs2)), xs)) -> app(app(app(app(filter2, app(app(app(app(filter2, app(fun10, x16)), fun10), x16), xs2)), c_app(filter, fun10)), c_app(c_app(cons, x16), xs2)), xs) [2]
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, c_app(fun, x)), fun), x), xs) [1]
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, null_app), fun), x), xs) [1]
   encArg(g) -> g [0]
   encArg(h) -> h [0]
   encArg(f) -> f [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_g -> g [0]
   encode_h -> h [0]
   encode_f -> f [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_g -> null_encode_g [0]
   encode_h -> null_encode_h [0]
   encode_f -> null_encode_f [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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app

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

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

   map => 7
   cons => 0
   g => 5
   h => 6
   f => 1
   filter2 => 4
   true => 9
   filter => 3
   false => 2
   nil => 8
   null_encArg => 0
   null_encode_app => 0
   null_encode_g => 0
   null_encode_h => 0
   null_encode_f => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_filter => 0
   null_encode_filter2 => 0
   null_encode_true => 0
   null_encode_false => 0
   null_app => 0

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

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

   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(app(app(4, app(fun10, x16)), fun10), x16), xs2)), 1 + 3 + fun10), 1 + (1 + 0 + x16) + xs2), xs) :|: z = 1 + 3 + (1 + 3 + fun10), xs >= 0, xs2 >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x16) + xs2)) + xs, fun10 >= 0, x16 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(3, fun7), x)), 1 + (1 + (1 + 4 + 2) + fun7) + x14), x), xs) :|: xs >= 0, z = 1 + 3 + (1 + (1 + (1 + 4 + 2) + fun7) + x14), x >= 0, x14 >= 0, z' = 1 + (1 + 0 + x) + xs, fun7 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(0, x13), app(app(3, fun6), x))), 1 + (1 + (1 + 4 + 9) + fun6) + x13), x), xs) :|: z = 1 + 3 + (1 + (1 + (1 + 4 + 9) + fun6) + x13), fun6 >= 0, x13 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(0, app(fun5, x10)), app(app(7, fun5), xs1))), 1 + 7 + fun5), 1 + (1 + 0 + x10) + xs1), xs) :|: xs >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x10) + xs1)) + xs, xs1 >= 0, z = 1 + 3 + (1 + 7 + fun5), fun5 >= 0, x10 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(6, app(app(1, app(6, x12)), x12))), 6), 1 + 6 + x12), xs) :|: z = 1 + 3 + 6, xs >= 0, z' = 1 + (1 + 0 + (1 + 6 + x12)) + xs, x12 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(5, x11)), 5), 1 + 6 + (1 + 5 + x11)), xs) :|: z' = 1 + (1 + 0 + (1 + 6 + (1 + 5 + x11))) + xs, xs >= 0, z = 1 + 3 + 5, x11 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(5, app(6, app(5, x15)))), 5), 1 + 5 + x15), xs) :|: z' = 1 + (1 + 0 + (1 + 5 + x15)) + xs, xs >= 0, z = 1 + 3 + 5, x15 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 7 + fun8), 8), xs) :|: xs >= 0, z' = 1 + (1 + 0 + 8) + xs, fun8 >= 0, z = 1 + 3 + (1 + 7 + fun8)
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 3 + fun9), 8), xs) :|: xs >= 0, z' = 1 + (1 + 0 + 8) + xs, z = 1 + 3 + (1 + 3 + fun9), fun9 >= 0
   app(z, z') -{ 1 }-> app(app(app(app(4, 0), fun), x), xs) :|: fun >= 0, xs >= 0, x >= 0, z = 1 + 3 + fun, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(app(4, 1 + fun + x), fun), x), xs) :|: fun >= 0, xs >= 0, x >= 0, z = 1 + 3 + fun, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, app(fun, x)), app(app(7, fun), xs)) :|: fun >= 0, xs >= 0, z = 1 + 7 + fun, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(6, app(app(1, app(6, app(app(1, app(6, x7)), x7))), 1 + 6 + x7)) :|: x7 >= 0, z = 6, z' = 1 + 6 + (1 + 6 + x7)
   app(z, z') -{ 1 }-> app(6, app(app(1, 0), x)) :|: x >= 0, z = 6, z' = 1 + 6 + x
   app(z, z') -{ 1 }-> app(6, app(app(1, 1 + 6 + x), x)) :|: x >= 0, z = 6, z' = 1 + 6 + x
   app(z, z') -{ 1 }-> app(5, x) :|: z' = 1 + 6 + (1 + 5 + x), x >= 0, z = 5
   app(z, z') -{ 2 }-> app(5, app(6, app(5, x8))) :|: x8 >= 0, z' = 1 + 5 + (1 + 6 + (1 + 5 + x8)), z = 5
   app(z, z') -{ 2 }-> app(5, app(6, app(5, app(6, app(5, x9))))) :|: z' = 1 + 5 + (1 + 5 + x9), z = 5, x9 >= 0
   app(z, z') -{ 1 }-> app(5, app(6, 0)) :|: z' = 1 + 5 + x, x >= 0, z = 5
   app(z, z') -{ 1 }-> app(5, app(6, 1 + 5 + x)) :|: z' = 1 + 5 + x, x >= 0, z = 5
   app(z, z') -{ 1 }-> app(0, xs) :|: z = 1 + (1 + (1 + 4 + 2) + fun) + x, fun >= 0, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(0, app(0, xs)) :|: fun >= 0, xs >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(0, app(1 + 3 + fun, xs)) :|: fun >= 0, xs >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(1 + 3 + fun, xs) :|: z = 1 + (1 + (1 + 4 + 2) + fun) + x, fun >= 0, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(1 + 0 + x, app(0, xs)) :|: fun >= 0, xs >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(1 + 0 + x, app(1 + 3 + fun, xs)) :|: fun >= 0, xs >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0, z' = xs
   app(z, z') -{ 1 }-> 8 :|: fun >= 0, z = 1 + 7 + fun, z' = 8
   app(z, z') -{ 1 }-> 8 :|: fun >= 0, z = 1 + 3 + fun, z' = 8
   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 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   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 }-> 0 :|: 
   encode_f -{ 0 }-> 1 :|: 
   encode_f -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_g -{ 0 }-> 5 :|: 
   encode_g -{ 0 }-> 0 :|: 
   encode_h -{ 0 }-> 6 :|: 
   encode_h -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 7 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 8 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 9 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

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

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

   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(app(app(4, app(z - 8, x16)), z - 8), x16), xs2)), 1 + 3 + (z - 8)), 1 + (1 + 0 + x16) + xs2), xs) :|: xs >= 0, xs2 >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x16) + xs2)) + xs, z - 8 >= 0, x16 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(3, fun7), x)), 1 + (1 + (1 + 4 + 2) + fun7) + x14), x), xs) :|: xs >= 0, z = 1 + 3 + (1 + (1 + (1 + 4 + 2) + fun7) + x14), x >= 0, x14 >= 0, z' = 1 + (1 + 0 + x) + xs, fun7 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(0, x13), app(app(3, fun6), x))), 1 + (1 + (1 + 4 + 9) + fun6) + x13), x), xs) :|: z = 1 + 3 + (1 + (1 + (1 + 4 + 9) + fun6) + x13), fun6 >= 0, x13 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(0, app(z - 12, x10)), app(app(7, z - 12), xs1))), 1 + 7 + (z - 12)), 1 + (1 + 0 + x10) + xs1), xs) :|: xs >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x10) + xs1)) + xs, xs1 >= 0, z - 12 >= 0, x10 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(6, app(app(1, app(6, x12)), x12))), 6), 1 + 6 + x12), xs) :|: z = 1 + 3 + 6, xs >= 0, z' = 1 + (1 + 0 + (1 + 6 + x12)) + xs, x12 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(5, x11)), 5), 1 + 6 + (1 + 5 + x11)), xs) :|: z' = 1 + (1 + 0 + (1 + 6 + (1 + 5 + x11))) + xs, xs >= 0, z = 1 + 3 + 5, x11 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(5, app(6, app(5, x15)))), 5), 1 + 5 + x15), xs) :|: z' = 1 + (1 + 0 + (1 + 5 + x15)) + xs, xs >= 0, z = 1 + 3 + 5, x15 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 7 + (z - 12)), 8), z' - 10) :|: z' - 10 >= 0, z - 12 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 3 + (z - 8)), 8), z' - 10) :|: z' - 10 >= 0, z - 8 >= 0
   app(z, z') -{ 1 }-> app(app(app(app(4, 0), z - 4), x), xs) :|: z - 4 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(app(4, 1 + (z - 4) + x), z - 4), x), xs) :|: z - 4 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, app(z - 8, x)), app(app(7, z - 8), xs)) :|: z - 8 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(6, app(app(1, app(6, app(app(1, app(6, z' - 14)), z' - 14))), 1 + 6 + (z' - 14))) :|: z' - 14 >= 0, z = 6
   app(z, z') -{ 1 }-> app(6, app(app(1, 0), z' - 7)) :|: z' - 7 >= 0, z = 6
   app(z, z') -{ 1 }-> app(6, app(app(1, 1 + 6 + (z' - 7)), z' - 7)) :|: z' - 7 >= 0, z = 6
   app(z, z') -{ 2 }-> app(5, app(6, app(5, app(6, app(5, z' - 12))))) :|: z = 5, z' - 12 >= 0
   app(z, z') -{ 2 }-> app(5, app(6, app(5, z' - 19))) :|: z' - 19 >= 0, z = 5
   app(z, z') -{ 1 }-> app(5, app(6, 0)) :|: z' - 6 >= 0, z = 5
   app(z, z') -{ 1 }-> app(5, app(6, 1 + 5 + (z' - 6))) :|: z' - 6 >= 0, z = 5
   app(z, z') -{ 1 }-> app(5, z' - 13) :|: z' - 13 >= 0, z = 5
   app(z, z') -{ 1 }-> app(0, z') :|: z = 1 + (1 + (1 + 4 + 2) + fun) + x, fun >= 0, z' >= 0, x >= 0
   app(z, z') -{ 1 }-> app(0, app(0, z')) :|: fun >= 0, z' >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0
   app(z, z') -{ 1 }-> app(0, app(1 + 3 + fun, z')) :|: fun >= 0, z' >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0
   app(z, z') -{ 1 }-> app(1 + 3 + fun, z') :|: z = 1 + (1 + (1 + 4 + 2) + fun) + x, fun >= 0, z' >= 0, x >= 0
   app(z, z') -{ 1 }-> app(1 + 0 + x, app(0, z')) :|: fun >= 0, z' >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0
   app(z, z') -{ 1 }-> app(1 + 0 + x, app(1 + 3 + fun, z')) :|: fun >= 0, z' >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0
   app(z, z') -{ 1 }-> 8 :|: z - 8 >= 0, z' = 8
   app(z, z') -{ 1 }-> 8 :|: z - 4 >= 0, z' = 8
   app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   app(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 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 }-> 0 :|: 
   encode_f -{ 0 }-> 1 :|: 
   encode_f -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_g -{ 0 }-> 5 :|: 
   encode_g -{ 0 }-> 0 :|: 
   encode_h -{ 0 }-> 6 :|: 
   encode_h -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 7 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 8 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 9 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

(31) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_g -> null_encode_g [0]
   encode_h -> null_encode_h [0]
   encode_f -> null_encode_f [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_g, null_encode_h, null_encode_f, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app

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

(32)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

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

   app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1]
   app(g, c_app(h, c_app(g, x))) -> app(g, x) [1]
   app(h, c_app(h, x)) -> app(h, app(app(f, app(h, x)), x)) [1]
   app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1]
   app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1]
   app(g, c_app(g, x)) -> app(g, app(h, app(g, x))) [1]
   app(c_app(map, fun), nil) -> nil [1]
   app(c_app(filter, fun), nil) -> nil [1]
   app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1]
   encArg(g) -> g [0]
   encArg(h) -> h [0]
   encArg(f) -> f [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_g -> g [0]
   encode_h -> h [0]
   encode_f -> f [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_g -> null_encode_g [0]
   encode_h -> null_encode_h [0]
   encode_f -> null_encode_f [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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_g :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_h :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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_f :: map:c_app:cons:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f: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:g:h:f:filter2:true:filter:false:nil:cons_app:null_encArg:null_encode_app:null_encode_g:null_encode_h:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app

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

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

   map => 7
   cons => 0
   g => 5
   h => 6
   f => 1
   filter2 => 4
   true => 9
   filter => 3
   false => 2
   nil => 8
   null_encArg => 0
   null_encode_app => 0
   null_encode_g => 0
   null_encode_h => 0
   null_encode_f => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_filter => 0
   null_encode_filter2 => 0
   null_encode_true => 0
   null_encode_false => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> app(app(app(app(4, app(fun, x)), fun), x), xs) :|: fun >= 0, xs >= 0, x >= 0, z = 1 + 3 + fun, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(3, fun), xs) :|: z = 1 + (1 + (1 + 4 + 2) + fun) + x, fun >= 0, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(app(0, x), app(app(3, fun), xs)) :|: fun >= 0, xs >= 0, z = 1 + (1 + (1 + 4 + 9) + fun) + x, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(app(0, app(fun, x)), app(app(7, fun), xs)) :|: fun >= 0, xs >= 0, z = 1 + 7 + fun, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(6, app(app(1, app(6, x)), x)) :|: x >= 0, z = 6, z' = 1 + 6 + x
   app(z, z') -{ 1 }-> app(5, x) :|: z' = 1 + 6 + (1 + 5 + x), x >= 0, z = 5
   app(z, z') -{ 1 }-> app(5, app(6, app(5, x))) :|: z' = 1 + 5 + x, x >= 0, z = 5
   app(z, z') -{ 1 }-> 8 :|: fun >= 0, z = 1 + 7 + fun, z' = 8
   app(z, z') -{ 1 }-> 8 :|: fun >= 0, z = 1 + 3 + fun, z' = 8
   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 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   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 }-> 0 :|: 
   encode_f -{ 0 }-> 1 :|: 
   encode_f -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_g -{ 0 }-> 5 :|: 
   encode_g -{ 0 }-> 0 :|: 
   encode_h -{ 0 }-> 6 :|: 
   encode_h -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 7 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 8 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 9 :|: 
   encode_true -{ 0 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.

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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g) -> c
   ENCARG(h) -> c1
   ENCARG(f) -> c2
   ENCARG(map) -> c3
   ENCARG(nil) -> c4
   ENCARG(cons) -> c5
   ENCARG(filter) -> c6
   ENCARG(filter2) -> c7
   ENCARG(true) -> c8
   ENCARG(false) -> c9
   ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_G -> c12
   ENCODE_H -> c13
   ENCODE_F -> c14
   ENCODE_MAP -> c15
   ENCODE_NIL -> c16
   ENCODE_CONS -> c17
   ENCODE_FILTER -> c18
   ENCODE_FILTER2 -> c19
   ENCODE_TRUE -> c20
   ENCODE_FALSE -> c21
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(h, app(g, z0)), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, app(app(f, app(h, z0)), z0)), APP(app(f, app(h, z0)), z0), APP(f, app(h, z0)), APP(h, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(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) -> c27
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(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) -> c29(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) -> c30(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(h, app(g, z0)), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, app(app(f, app(h, z0)), z0)), APP(app(f, app(h, z0)), z0), APP(f, app(h, z0)), APP(h, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(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) -> c27
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(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) -> c29(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) -> c30(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_g, encode_h, encode_f, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_G, ENCODE_H, ENCODE_F, 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_3, c11_3, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22_1, c23_3, c24_4, c25, c26_5, c27, c28_5, c29_4, c30_2


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

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 20 trailing nodes:
   ENCODE_G -> c12
   ENCODE_TRUE -> c20
   ENCODE_MAP -> c15
   ENCARG(true) -> c8
   ENCARG(filter2) -> c7
   ENCARG(map) -> c3
   ENCARG(g) -> c
   ENCODE_FALSE -> c21
   ENCODE_FILTER2 -> c19
   ENCARG(false) -> c9
   ENCARG(f) -> c2
   ENCARG(filter) -> c6
   ENCARG(nil) -> c4
   ENCODE_CONS -> c17
   ENCODE_F -> c14
   ENCARG(h) -> c1
   ENCODE_H -> c13
   ENCODE_NIL -> c16
   ENCARG(cons) -> c5
   ENCODE_FILTER -> c18

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(h, app(g, z0)), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, app(app(f, app(h, z0)), z0)), APP(app(f, app(h, z0)), z0), APP(f, app(h, z0)), APP(h, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(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) -> c27
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(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) -> c29(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) -> c30(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(h, app(g, z0)), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, app(app(f, app(h, z0)), z0)), APP(app(f, app(h, z0)), z0), APP(f, app(h, z0)), APP(h, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(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) -> c27
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(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) -> c29(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) -> c30(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_g, encode_h, encode_f, 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:   c10_3, c11_3, c22_1, c23_3, c24_4, c25, c26_5, c27, c28_5, c29_4, c30_2


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

(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 14 trailing tuple parts
----------------------------------------

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_g, encode_h, encode_f, 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:   c10_3, c11_3, c22_1, c25, c27, c23_2, c24_1, c26_2, c28_2, c29_1, c30_1


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_g, encode_h, encode_f, 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:   c10_3, c22_1, c25, c27, c23_2, c24_1, c26_2, c28_2, c29_1, c30_1, c_1


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

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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_g, encode_h, encode_f, 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:   c10_3, c22_1, c25, c27, c23_2, c24_1, c26_2, c28_2, c29_1, c30_1, c_1


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

(45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_g -> g
   encode_h -> h
   encode_f -> f
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(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:   c10_3, c22_1, c25, c27, c23_2, c24_1, c26_2, c28_2, c29_1, c30_1, c_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0), ENCARG(g))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0), ENCARG(h))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0), ENCARG(f))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(g), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(h), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(APP(f, encArg(x1)), ENCARG(f), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0), ENCARG(g))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0), ENCARG(h))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0), ENCARG(f))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(g), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(h), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(APP(f, encArg(x1)), ENCARG(f), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c28_2, c29_1, c30_1, c_1, c10_3


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

(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 28 trailing tuple parts
----------------------------------------

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c28_2, c29_1, c30_1, c_1, c10_3, c10_2, c10_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c28(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by 
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(app(app(app(filter2, app(g, z0)), g), app(h, app(g, z0))), x2), APP(g, app(h, app(g, z0))))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(app(app(app(filter2, app(h, app(app(f, app(h, z0)), z0))), h), app(h, z0)), x2), APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(app(app(app(filter2, app(g, z0)), g), app(h, app(g, z0))), x2), APP(g, app(h, app(g, z0))))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(app(app(app(filter2, app(h, app(app(f, app(h, z0)), z0))), h), app(h, z0)), x2), APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(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)) -> c28(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)) -> c28(APP(app(app(app(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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(app(app(app(filter2, app(g, z0)), g), app(h, app(g, z0))), x2), APP(g, app(h, app(g, z0))))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(app(app(app(filter2, app(h, app(app(f, app(h, z0)), z0))), h), app(h, z0)), x2), APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(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)) -> c28(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)) -> c28(APP(app(app(app(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c_1, c10_3, c10_2, c10_1, c28_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c_1, c10_3, c10_2, c10_1, c28_2, c28_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(f, x1) -> c(APP(f, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(f, x1) -> c(APP(f, 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_3, c10_2, c10_1, c28_2, c28_1, c_1


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(f, x1) -> c(APP(f, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_3, c10_2, c10_1, c28_2, c28_1, c_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(g), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(h), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(APP(f, app(encArg(x1), encArg(x2))), ENCARG(f), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(g), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(h), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(APP(f, app(encArg(x1), encArg(x2))), ENCARG(f), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_3, c10_2, c10_1, c28_2, c28_1, c_1


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

(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 18 trailing tuple parts
----------------------------------------

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_3, c10_2, c10_1, c28_2, c28_1, c_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)), ENCARG(g))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)), ENCARG(h))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)), ENCARG(f))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(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))) -> c10(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, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(APP(app(f, encArg(x1)), encArg(x2)), ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(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)) -> c10(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)), ENCARG(g))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)), ENCARG(h))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)), ENCARG(f))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(APP(app(f, encArg(x1)), encArg(x2)), ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(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)) -> c10(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 16 trailing tuple parts
----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, g)) -> c10(APP(encArg(x0), g), ENCARG(x0)) by 
   ENCARG(cons_app(g, g)) -> c10(APP(g, g), ENCARG(g))
   ENCARG(cons_app(h, g)) -> c10(APP(h, g), ENCARG(h))
   ENCARG(cons_app(f, g)) -> c10(APP(f, g), ENCARG(f))
   ENCARG(cons_app(map, g)) -> c10(APP(map, g), ENCARG(map))
   ENCARG(cons_app(nil, g)) -> c10(APP(nil, g), ENCARG(nil))
   ENCARG(cons_app(cons, g)) -> c10(APP(cons, g), ENCARG(cons))
   ENCARG(cons_app(filter, g)) -> c10(APP(filter, g), ENCARG(filter))
   ENCARG(cons_app(filter2, g)) -> c10(APP(filter2, g), ENCARG(filter2))
   ENCARG(cons_app(true, g)) -> c10(APP(true, g), ENCARG(true))
   ENCARG(cons_app(false, g)) -> c10(APP(false, g), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), g)) -> c10(APP(app(encArg(z0), encArg(z1)), g), ENCARG(cons_app(z0, z1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, g)) -> c10(APP(g, g), ENCARG(g))
   ENCARG(cons_app(h, g)) -> c10(APP(h, g), ENCARG(h))
   ENCARG(cons_app(f, g)) -> c10(APP(f, g), ENCARG(f))
   ENCARG(cons_app(map, g)) -> c10(APP(map, g), ENCARG(map))
   ENCARG(cons_app(nil, g)) -> c10(APP(nil, g), ENCARG(nil))
   ENCARG(cons_app(cons, g)) -> c10(APP(cons, g), ENCARG(cons))
   ENCARG(cons_app(filter, g)) -> c10(APP(filter, g), ENCARG(filter))
   ENCARG(cons_app(filter2, g)) -> c10(APP(filter2, g), ENCARG(filter2))
   ENCARG(cons_app(true, g)) -> c10(APP(true, g), ENCARG(true))
   ENCARG(cons_app(false, g)) -> c10(APP(false, g), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(filter2, g)) -> c10(APP(filter2, g), ENCARG(filter2))
   ENCARG(cons_app(map, g)) -> c10(APP(map, g), ENCARG(map))
   ENCARG(cons_app(cons, g)) -> c10(APP(cons, g), ENCARG(cons))
   ENCARG(cons_app(nil, g)) -> c10(APP(nil, g), ENCARG(nil))
   ENCARG(cons_app(true, g)) -> c10(APP(true, g), ENCARG(true))
   ENCARG(cons_app(g, g)) -> c10(APP(g, g), ENCARG(g))
   ENCARG(cons_app(h, g)) -> c10(APP(h, g), ENCARG(h))
   ENCARG(cons_app(false, g)) -> c10(APP(false, g), ENCARG(false))
   ENCARG(cons_app(filter, g)) -> c10(APP(filter, g), ENCARG(filter))
   ENCARG(cons_app(f, g)) -> c10(APP(f, g), ENCARG(f))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, h)) -> c10(APP(encArg(x0), h), ENCARG(x0)) by 
   ENCARG(cons_app(g, h)) -> c10(APP(g, h), ENCARG(g))
   ENCARG(cons_app(h, h)) -> c10(APP(h, h), ENCARG(h))
   ENCARG(cons_app(f, h)) -> c10(APP(f, h), ENCARG(f))
   ENCARG(cons_app(map, h)) -> c10(APP(map, h), ENCARG(map))
   ENCARG(cons_app(nil, h)) -> c10(APP(nil, h), ENCARG(nil))
   ENCARG(cons_app(cons, h)) -> c10(APP(cons, h), ENCARG(cons))
   ENCARG(cons_app(filter, h)) -> c10(APP(filter, h), ENCARG(filter))
   ENCARG(cons_app(filter2, h)) -> c10(APP(filter2, h), ENCARG(filter2))
   ENCARG(cons_app(true, h)) -> c10(APP(true, h), ENCARG(true))
   ENCARG(cons_app(false, h)) -> c10(APP(false, h), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), h)) -> c10(APP(app(encArg(z0), encArg(z1)), h), ENCARG(cons_app(z0, z1)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, h)) -> c10(APP(g, h), ENCARG(g))
   ENCARG(cons_app(h, h)) -> c10(APP(h, h), ENCARG(h))
   ENCARG(cons_app(f, h)) -> c10(APP(f, h), ENCARG(f))
   ENCARG(cons_app(map, h)) -> c10(APP(map, h), ENCARG(map))
   ENCARG(cons_app(nil, h)) -> c10(APP(nil, h), ENCARG(nil))
   ENCARG(cons_app(cons, h)) -> c10(APP(cons, h), ENCARG(cons))
   ENCARG(cons_app(filter, h)) -> c10(APP(filter, h), ENCARG(filter))
   ENCARG(cons_app(filter2, h)) -> c10(APP(filter2, h), ENCARG(filter2))
   ENCARG(cons_app(true, h)) -> c10(APP(true, h), ENCARG(true))
   ENCARG(cons_app(false, h)) -> c10(APP(false, h), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(f, h)) -> c10(APP(f, h), ENCARG(f))
   ENCARG(cons_app(filter, h)) -> c10(APP(filter, h), ENCARG(filter))
   ENCARG(cons_app(h, h)) -> c10(APP(h, h), ENCARG(h))
   ENCARG(cons_app(filter2, h)) -> c10(APP(filter2, h), ENCARG(filter2))
   ENCARG(cons_app(map, h)) -> c10(APP(map, h), ENCARG(map))
   ENCARG(cons_app(false, h)) -> c10(APP(false, h), ENCARG(false))
   ENCARG(cons_app(g, h)) -> c10(APP(g, h), ENCARG(g))
   ENCARG(cons_app(cons, h)) -> c10(APP(cons, h), ENCARG(cons))
   ENCARG(cons_app(true, h)) -> c10(APP(true, h), ENCARG(true))
   ENCARG(cons_app(nil, h)) -> c10(APP(nil, h), ENCARG(nil))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, f)) -> c10(APP(encArg(x0), f), ENCARG(x0)) by 
   ENCARG(cons_app(g, f)) -> c10(APP(g, f), ENCARG(g))
   ENCARG(cons_app(h, f)) -> c10(APP(h, f), ENCARG(h))
   ENCARG(cons_app(f, f)) -> c10(APP(f, f), ENCARG(f))
   ENCARG(cons_app(map, f)) -> c10(APP(map, f), ENCARG(map))
   ENCARG(cons_app(nil, f)) -> c10(APP(nil, f), ENCARG(nil))
   ENCARG(cons_app(cons, f)) -> c10(APP(cons, f), ENCARG(cons))
   ENCARG(cons_app(filter, f)) -> c10(APP(filter, f), ENCARG(filter))
   ENCARG(cons_app(filter2, f)) -> c10(APP(filter2, f), ENCARG(filter2))
   ENCARG(cons_app(true, f)) -> c10(APP(true, f), ENCARG(true))
   ENCARG(cons_app(false, f)) -> c10(APP(false, f), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), f)) -> c10(APP(app(encArg(z0), encArg(z1)), f), ENCARG(cons_app(z0, z1)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, f)) -> c10(APP(g, f), ENCARG(g))
   ENCARG(cons_app(h, f)) -> c10(APP(h, f), ENCARG(h))
   ENCARG(cons_app(f, f)) -> c10(APP(f, f), ENCARG(f))
   ENCARG(cons_app(map, f)) -> c10(APP(map, f), ENCARG(map))
   ENCARG(cons_app(nil, f)) -> c10(APP(nil, f), ENCARG(nil))
   ENCARG(cons_app(cons, f)) -> c10(APP(cons, f), ENCARG(cons))
   ENCARG(cons_app(filter, f)) -> c10(APP(filter, f), ENCARG(filter))
   ENCARG(cons_app(filter2, f)) -> c10(APP(filter2, f), ENCARG(filter2))
   ENCARG(cons_app(true, f)) -> c10(APP(true, f), ENCARG(true))
   ENCARG(cons_app(false, f)) -> c10(APP(false, f), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(g, f)) -> c10(APP(g, f), ENCARG(g))
   ENCARG(cons_app(h, f)) -> c10(APP(h, f), ENCARG(h))
   ENCARG(cons_app(filter2, f)) -> c10(APP(filter2, f), ENCARG(filter2))
   ENCARG(cons_app(map, f)) -> c10(APP(map, f), ENCARG(map))
   ENCARG(cons_app(false, f)) -> c10(APP(false, f), ENCARG(false))
   ENCARG(cons_app(cons, f)) -> c10(APP(cons, f), ENCARG(cons))
   ENCARG(cons_app(filter, f)) -> c10(APP(filter, f), ENCARG(filter))
   ENCARG(cons_app(f, f)) -> c10(APP(f, f), ENCARG(f))
   ENCARG(cons_app(nil, f)) -> c10(APP(nil, f), ENCARG(nil))
   ENCARG(cons_app(true, f)) -> c10(APP(true, f), ENCARG(true))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) by 
   ENCARG(cons_app(g, map)) -> c10(APP(g, map), ENCARG(g))
   ENCARG(cons_app(h, map)) -> c10(APP(h, map), ENCARG(h))
   ENCARG(cons_app(f, map)) -> c10(APP(f, map), ENCARG(f))
   ENCARG(cons_app(map, map)) -> c10(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c10(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c10(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c10(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c10(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(true, map)) -> c10(APP(true, map), ENCARG(true))
   ENCARG(cons_app(false, map)) -> c10(APP(false, map), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), map)) -> c10(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1)))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, map)) -> c10(APP(g, map), ENCARG(g))
   ENCARG(cons_app(h, map)) -> c10(APP(h, map), ENCARG(h))
   ENCARG(cons_app(f, map)) -> c10(APP(f, map), ENCARG(f))
   ENCARG(cons_app(map, map)) -> c10(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c10(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c10(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c10(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c10(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(true, map)) -> c10(APP(true, map), ENCARG(true))
   ENCARG(cons_app(false, map)) -> c10(APP(false, map), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(filter, map)) -> c10(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(cons, map)) -> c10(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(nil, map)) -> c10(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(true, map)) -> c10(APP(true, map), ENCARG(true))
   ENCARG(cons_app(g, map)) -> c10(APP(g, map), ENCARG(g))
   ENCARG(cons_app(false, map)) -> c10(APP(false, map), ENCARG(false))
   ENCARG(cons_app(h, map)) -> c10(APP(h, map), ENCARG(h))
   ENCARG(cons_app(f, map)) -> c10(APP(f, map), ENCARG(f))
   ENCARG(cons_app(filter2, map)) -> c10(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(map, map)) -> c10(APP(map, map), ENCARG(map))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(g, nil)) -> c10(APP(g, nil), ENCARG(g))
   ENCARG(cons_app(h, nil)) -> c10(APP(h, nil), ENCARG(h))
   ENCARG(cons_app(f, nil)) -> c10(APP(f, nil), ENCARG(f))
   ENCARG(cons_app(map, nil)) -> c10(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c10(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c10(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c10(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c10(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(true, nil)) -> c10(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c10(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c10(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, nil)) -> c10(APP(g, nil), ENCARG(g))
   ENCARG(cons_app(h, nil)) -> c10(APP(h, nil), ENCARG(h))
   ENCARG(cons_app(f, nil)) -> c10(APP(f, nil), ENCARG(f))
   ENCARG(cons_app(map, nil)) -> c10(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c10(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c10(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c10(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c10(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(true, nil)) -> c10(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c10(APP(false, nil), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(h, nil)) -> c10(APP(h, nil), ENCARG(h))
   ENCARG(cons_app(false, nil)) -> c10(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(g, nil)) -> c10(APP(g, nil), ENCARG(g))
   ENCARG(cons_app(true, nil)) -> c10(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(filter2, nil)) -> c10(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(map, nil)) -> c10(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c10(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(filter, nil)) -> c10(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(f, nil)) -> c10(APP(f, nil), ENCARG(f))
   ENCARG(cons_app(cons, nil)) -> c10(APP(cons, nil), ENCARG(cons))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(g, cons)) -> c10(APP(g, cons), ENCARG(g))
   ENCARG(cons_app(h, cons)) -> c10(APP(h, cons), ENCARG(h))
   ENCARG(cons_app(f, cons)) -> c10(APP(f, cons), ENCARG(f))
   ENCARG(cons_app(map, cons)) -> c10(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c10(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c10(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c10(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c10(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(true, cons)) -> c10(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c10(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c10(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, cons)) -> c10(APP(g, cons), ENCARG(g))
   ENCARG(cons_app(h, cons)) -> c10(APP(h, cons), ENCARG(h))
   ENCARG(cons_app(f, cons)) -> c10(APP(f, cons), ENCARG(f))
   ENCARG(cons_app(map, cons)) -> c10(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c10(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c10(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c10(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c10(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(true, cons)) -> c10(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c10(APP(false, cons), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(false, cons)) -> c10(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(f, cons)) -> c10(APP(f, cons), ENCARG(f))
   ENCARG(cons_app(filter, cons)) -> c10(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(true, cons)) -> c10(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(nil, cons)) -> c10(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(g, cons)) -> c10(APP(g, cons), ENCARG(g))
   ENCARG(cons_app(filter2, cons)) -> c10(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(map, cons)) -> c10(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(cons, cons)) -> c10(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(h, cons)) -> c10(APP(h, cons), ENCARG(h))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) by 
   ENCARG(cons_app(g, filter)) -> c10(APP(g, filter), ENCARG(g))
   ENCARG(cons_app(h, filter)) -> c10(APP(h, filter), ENCARG(h))
   ENCARG(cons_app(f, filter)) -> c10(APP(f, filter), ENCARG(f))
   ENCARG(cons_app(map, filter)) -> c10(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c10(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c10(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c10(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c10(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(true, filter)) -> c10(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(false, filter)) -> c10(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), filter)) -> c10(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, filter)) -> c10(APP(g, filter), ENCARG(g))
   ENCARG(cons_app(h, filter)) -> c10(APP(h, filter), ENCARG(h))
   ENCARG(cons_app(f, filter)) -> c10(APP(f, filter), ENCARG(f))
   ENCARG(cons_app(map, filter)) -> c10(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c10(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c10(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c10(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c10(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(true, filter)) -> c10(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(false, filter)) -> c10(APP(false, filter), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(nil, filter)) -> c10(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(filter, filter)) -> c10(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(cons, filter)) -> c10(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(false, filter)) -> c10(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(g, filter)) -> c10(APP(g, filter), ENCARG(g))
   ENCARG(cons_app(true, filter)) -> c10(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(h, filter)) -> c10(APP(h, filter), ENCARG(h))
   ENCARG(cons_app(filter2, filter)) -> c10(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(map, filter)) -> c10(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(f, filter)) -> c10(APP(f, filter), ENCARG(f))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) by 
   ENCARG(cons_app(g, filter2)) -> c10(APP(g, filter2), ENCARG(g))
   ENCARG(cons_app(h, filter2)) -> c10(APP(h, filter2), ENCARG(h))
   ENCARG(cons_app(f, filter2)) -> c10(APP(f, filter2), ENCARG(f))
   ENCARG(cons_app(map, filter2)) -> c10(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c10(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c10(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c10(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c10(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(true, filter2)) -> c10(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(false, filter2)) -> c10(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), filter2)) -> c10(APP(app(encArg(z0), encArg(z1)), filter2), ENCARG(cons_app(z0, z1)))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, filter2)) -> c10(APP(g, filter2), ENCARG(g))
   ENCARG(cons_app(h, filter2)) -> c10(APP(h, filter2), ENCARG(h))
   ENCARG(cons_app(f, filter2)) -> c10(APP(f, filter2), ENCARG(f))
   ENCARG(cons_app(map, filter2)) -> c10(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c10(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c10(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c10(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c10(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(true, filter2)) -> c10(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(false, filter2)) -> c10(APP(false, filter2), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(h, filter2)) -> c10(APP(h, filter2), ENCARG(h))
   ENCARG(cons_app(g, filter2)) -> c10(APP(g, filter2), ENCARG(g))
   ENCARG(cons_app(filter, filter2)) -> c10(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(nil, filter2)) -> c10(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(filter2, filter2)) -> c10(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(map, filter2)) -> c10(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(f, filter2)) -> c10(APP(f, filter2), ENCARG(f))
   ENCARG(cons_app(cons, filter2)) -> c10(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(false, filter2)) -> c10(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(true, filter2)) -> c10(APP(true, filter2), ENCARG(true))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) by 
   ENCARG(cons_app(g, true)) -> c10(APP(g, true), ENCARG(g))
   ENCARG(cons_app(h, true)) -> c10(APP(h, true), ENCARG(h))
   ENCARG(cons_app(f, true)) -> c10(APP(f, true), ENCARG(f))
   ENCARG(cons_app(map, true)) -> c10(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c10(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c10(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c10(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c10(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(true, true)) -> c10(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c10(APP(false, true), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), true)) -> c10(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, true)) -> c10(APP(g, true), ENCARG(g))
   ENCARG(cons_app(h, true)) -> c10(APP(h, true), ENCARG(h))
   ENCARG(cons_app(f, true)) -> c10(APP(f, true), ENCARG(f))
   ENCARG(cons_app(map, true)) -> c10(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c10(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c10(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c10(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c10(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(true, true)) -> c10(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c10(APP(false, true), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(filter2, true)) -> c10(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(map, true)) -> c10(APP(map, true), ENCARG(map))
   ENCARG(cons_app(true, true)) -> c10(APP(true, true), ENCARG(true))
   ENCARG(cons_app(nil, true)) -> c10(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(f, true)) -> c10(APP(f, true), ENCARG(f))
   ENCARG(cons_app(h, true)) -> c10(APP(h, true), ENCARG(h))
   ENCARG(cons_app(filter, true)) -> c10(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(false, true)) -> c10(APP(false, true), ENCARG(false))
   ENCARG(cons_app(g, true)) -> c10(APP(g, true), ENCARG(g))
   ENCARG(cons_app(cons, true)) -> c10(APP(cons, true), ENCARG(cons))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) by 
   ENCARG(cons_app(g, false)) -> c10(APP(g, false), ENCARG(g))
   ENCARG(cons_app(h, false)) -> c10(APP(h, false), ENCARG(h))
   ENCARG(cons_app(f, false)) -> c10(APP(f, false), ENCARG(f))
   ENCARG(cons_app(map, false)) -> c10(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c10(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c10(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c10(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c10(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(true, false)) -> c10(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c10(APP(false, false), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), false)) -> c10(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1)))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, false)) -> c10(APP(g, false), ENCARG(g))
   ENCARG(cons_app(h, false)) -> c10(APP(h, false), ENCARG(h))
   ENCARG(cons_app(f, false)) -> c10(APP(f, false), ENCARG(f))
   ENCARG(cons_app(map, false)) -> c10(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c10(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c10(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c10(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c10(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(true, false)) -> c10(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c10(APP(false, false), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(f, false)) -> c10(APP(f, false), ENCARG(f))
   ENCARG(cons_app(true, false)) -> c10(APP(true, false), ENCARG(true))
   ENCARG(cons_app(cons, false)) -> c10(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(nil, false)) -> c10(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(h, false)) -> c10(APP(h, false), ENCARG(h))
   ENCARG(cons_app(g, false)) -> c10(APP(g, false), ENCARG(g))
   ENCARG(cons_app(filter2, false)) -> c10(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(filter, false)) -> c10(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(map, false)) -> c10(APP(map, false), ENCARG(map))
   ENCARG(cons_app(false, false)) -> c10(APP(false, false), ENCARG(false))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(g, x1)) -> c10(APP(g, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_app(g, g)) -> c10(APP(g, g), ENCARG(g))
   ENCARG(cons_app(g, h)) -> c10(APP(g, h), ENCARG(h))
   ENCARG(cons_app(g, f)) -> c10(APP(g, f), ENCARG(f))
   ENCARG(cons_app(g, map)) -> c10(APP(g, map), ENCARG(map))
   ENCARG(cons_app(g, nil)) -> c10(APP(g, nil), ENCARG(nil))
   ENCARG(cons_app(g, cons)) -> c10(APP(g, cons), ENCARG(cons))
   ENCARG(cons_app(g, filter)) -> c10(APP(g, filter), ENCARG(filter))
   ENCARG(cons_app(g, filter2)) -> c10(APP(g, filter2), ENCARG(filter2))
   ENCARG(cons_app(g, true)) -> c10(APP(g, true), ENCARG(true))
   ENCARG(cons_app(g, false)) -> c10(APP(g, false), ENCARG(false))
   ENCARG(cons_app(g, cons_app(z0, z1))) -> c10(APP(g, app(encArg(z0), encArg(z1))), ENCARG(cons_app(z0, z1)))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(g, g)) -> c10(APP(g, g), ENCARG(g))
   ENCARG(cons_app(g, h)) -> c10(APP(g, h), ENCARG(h))
   ENCARG(cons_app(g, f)) -> c10(APP(g, f), ENCARG(f))
   ENCARG(cons_app(g, map)) -> c10(APP(g, map), ENCARG(map))
   ENCARG(cons_app(g, nil)) -> c10(APP(g, nil), ENCARG(nil))
   ENCARG(cons_app(g, cons)) -> c10(APP(g, cons), ENCARG(cons))
   ENCARG(cons_app(g, filter)) -> c10(APP(g, filter), ENCARG(filter))
   ENCARG(cons_app(g, filter2)) -> c10(APP(g, filter2), ENCARG(filter2))
   ENCARG(cons_app(g, true)) -> c10(APP(g, true), ENCARG(true))
   ENCARG(cons_app(g, false)) -> c10(APP(g, false), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(g, filter2)) -> c10(APP(g, filter2), ENCARG(filter2))
   ENCARG(cons_app(g, nil)) -> c10(APP(g, nil), ENCARG(nil))
   ENCARG(cons_app(g, map)) -> c10(APP(g, map), ENCARG(map))
   ENCARG(cons_app(g, false)) -> c10(APP(g, false), ENCARG(false))
   ENCARG(cons_app(g, cons)) -> c10(APP(g, cons), ENCARG(cons))
   ENCARG(cons_app(g, g)) -> c10(APP(g, g), ENCARG(g))
   ENCARG(cons_app(g, h)) -> c10(APP(g, h), ENCARG(h))
   ENCARG(cons_app(g, filter)) -> c10(APP(g, filter), ENCARG(filter))
   ENCARG(cons_app(g, true)) -> c10(APP(g, true), ENCARG(true))
   ENCARG(cons_app(g, f)) -> c10(APP(g, f), ENCARG(f))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_2, c10_1, c28_2, c28_1, c_1, c10_3


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(h, x1)) -> c10(APP(h, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_app(h, g)) -> c10(APP(h, g), ENCARG(g))
   ENCARG(cons_app(h, h)) -> c10(APP(h, h), ENCARG(h))
   ENCARG(cons_app(h, f)) -> c10(APP(h, f), ENCARG(f))
   ENCARG(cons_app(h, map)) -> c10(APP(h, map), ENCARG(map))
   ENCARG(cons_app(h, nil)) -> c10(APP(h, nil), ENCARG(nil))
   ENCARG(cons_app(h, cons)) -> c10(APP(h, cons), ENCARG(cons))
   ENCARG(cons_app(h, filter)) -> c10(APP(h, filter), ENCARG(filter))
   ENCARG(cons_app(h, filter2)) -> c10(APP(h, filter2), ENCARG(filter2))
   ENCARG(cons_app(h, true)) -> c10(APP(h, true), ENCARG(true))
   ENCARG(cons_app(h, false)) -> c10(APP(h, false), ENCARG(false))
   ENCARG(cons_app(h, cons_app(z0, z1))) -> c10(APP(h, app(encArg(z0), encArg(z1))), ENCARG(cons_app(z0, z1)))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(h, g)) -> c10(APP(h, g), ENCARG(g))
   ENCARG(cons_app(h, h)) -> c10(APP(h, h), ENCARG(h))
   ENCARG(cons_app(h, f)) -> c10(APP(h, f), ENCARG(f))
   ENCARG(cons_app(h, map)) -> c10(APP(h, map), ENCARG(map))
   ENCARG(cons_app(h, nil)) -> c10(APP(h, nil), ENCARG(nil))
   ENCARG(cons_app(h, cons)) -> c10(APP(h, cons), ENCARG(cons))
   ENCARG(cons_app(h, filter)) -> c10(APP(h, filter), ENCARG(filter))
   ENCARG(cons_app(h, filter2)) -> c10(APP(h, filter2), ENCARG(filter2))
   ENCARG(cons_app(h, true)) -> c10(APP(h, true), ENCARG(true))
   ENCARG(cons_app(h, false)) -> c10(APP(h, false), ENCARG(false))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_2, c28_1, c_1, c10_3, c10_2


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCARG(cons_app(h, false)) -> c10(APP(h, false), ENCARG(false))
   ENCARG(cons_app(h, true)) -> c10(APP(h, true), ENCARG(true))
   ENCARG(cons_app(h, g)) -> c10(APP(h, g), ENCARG(g))
   ENCARG(cons_app(h, cons)) -> c10(APP(h, cons), ENCARG(cons))
   ENCARG(cons_app(h, nil)) -> c10(APP(h, nil), ENCARG(nil))
   ENCARG(cons_app(h, filter)) -> c10(APP(h, filter), ENCARG(filter))
   ENCARG(cons_app(h, h)) -> c10(APP(h, h), ENCARG(h))
   ENCARG(cons_app(h, f)) -> c10(APP(h, f), ENCARG(f))
   ENCARG(cons_app(h, filter2)) -> c10(APP(h, filter2), ENCARG(filter2))
   ENCARG(cons_app(h, map)) -> c10(APP(h, map), ENCARG(map))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_2, c28_1, c_1, c10_3, c10_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, g), app(app(cons, app(g, z0)), x2)) -> c28(APP(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2), APP(g, app(g, z0))) by 
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(app(app(app(filter2, app(g, z0)), g), app(g, z0)), x1), APP(g, app(g, z0)))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(app(app(app(filter2, app(g, z0)), g), app(g, z0)), x1), APP(g, app(g, z0)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(app(app(app(filter2, app(g, z0)), g), app(g, z0)), x1), APP(g, app(g, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_2, c28_1, c_1, c10_3, c10_2


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

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_2, c28_1, c_1, c10_3, c10_2


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, 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)) -> c28(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)) -> c28(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, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, z0)), g), app(h, app(g, z0))), x2)), app(filter, g)), app(app(cons, app(h, app(g, z0))), x2)), x3), APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(h, app(app(f, app(h, z0)), z0))), h), app(h, z0)), x2)), app(filter, h)), app(app(cons, app(h, z0)), x2)), x3), APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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)) -> c28(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, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, z0)), g), app(h, app(g, z0))), x2)), app(filter, g)), app(app(cons, app(h, app(g, z0))), x2)), x3), APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(h, app(app(f, app(h, z0)), z0))), h), app(h, z0)), x2)), app(filter, h)), app(app(cons, app(h, z0)), x2)), x3), APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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)) -> c28(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, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, z0)), g), app(h, app(g, z0))), x2)), app(filter, g)), app(app(cons, app(h, app(g, z0))), x2)), x3), APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(h, app(app(f, app(h, z0)), z0))), h), app(h, z0)), x2)), app(filter, h)), app(app(cons, app(h, z0)), x2)), x3), APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_2, c28_1, c_1, c10_3, c10_2


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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_2, c28_1, c_1, c10_3, c10_2


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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(125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
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(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, g) -> c(APP(encArg(x0), g))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(g, g) -> c(APP(g, g))
   ENCODE_APP(h, g) -> c(APP(h, g))
   ENCODE_APP(f, g) -> c(APP(f, g))
   ENCODE_APP(map, g) -> c(APP(map, g))
   ENCODE_APP(nil, g) -> c(APP(nil, g))
   ENCODE_APP(cons, g) -> c(APP(cons, g))
   ENCODE_APP(filter, g) -> c(APP(filter, g))
   ENCODE_APP(filter2, g) -> c(APP(filter2, g))
   ENCODE_APP(true, g) -> c(APP(true, g))
   ENCODE_APP(false, g) -> c(APP(false, g))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCODE_APP(map, g) -> c(APP(map, g))
   ENCODE_APP(f, g) -> c(APP(f, g))
   ENCODE_APP(true, g) -> c(APP(true, g))
   ENCODE_APP(h, g) -> c(APP(h, g))
   ENCODE_APP(filter2, g) -> c(APP(filter2, g))
   ENCODE_APP(cons, g) -> c(APP(cons, g))
   ENCODE_APP(false, g) -> c(APP(false, g))
   ENCODE_APP(filter, g) -> c(APP(filter, g))
   ENCODE_APP(nil, g) -> c(APP(nil, g))
   ENCODE_APP(g, g) -> c(APP(g, g))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, h) -> c(APP(encArg(x0), h))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(g, h) -> c(APP(g, h))
   ENCODE_APP(h, h) -> c(APP(h, h))
   ENCODE_APP(f, h) -> c(APP(f, h))
   ENCODE_APP(map, h) -> c(APP(map, h))
   ENCODE_APP(nil, h) -> c(APP(nil, h))
   ENCODE_APP(cons, h) -> c(APP(cons, h))
   ENCODE_APP(filter, h) -> c(APP(filter, h))
   ENCODE_APP(filter2, h) -> c(APP(filter2, h))
   ENCODE_APP(true, h) -> c(APP(true, h))
   ENCODE_APP(false, h) -> c(APP(false, h))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCODE_APP(g, h) -> c(APP(g, h))
   ENCODE_APP(cons, h) -> c(APP(cons, h))
   ENCODE_APP(h, h) -> c(APP(h, h))
   ENCODE_APP(nil, h) -> c(APP(nil, h))
   ENCODE_APP(false, h) -> c(APP(false, h))
   ENCODE_APP(filter2, h) -> c(APP(filter2, h))
   ENCODE_APP(map, h) -> c(APP(map, h))
   ENCODE_APP(f, h) -> c(APP(f, h))
   ENCODE_APP(true, h) -> c(APP(true, h))
   ENCODE_APP(filter, h) -> c(APP(filter, h))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, f) -> c(APP(encArg(x0), f))
   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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
   ENCODE_APP(g, f) -> c(APP(g, f))
   ENCODE_APP(h, f) -> c(APP(h, f))
   ENCODE_APP(f, f) -> c(APP(f, f))
   ENCODE_APP(map, f) -> c(APP(map, f))
   ENCODE_APP(nil, f) -> c(APP(nil, f))
   ENCODE_APP(cons, f) -> c(APP(cons, f))
   ENCODE_APP(filter, f) -> c(APP(filter, f))
   ENCODE_APP(filter2, f) -> c(APP(filter2, f))
   ENCODE_APP(true, f) -> c(APP(true, f))
   ENCODE_APP(false, f) -> c(APP(false, f))
   ENCODE_APP(cons_app(z0, z1), f) -> c(APP(app(encArg(z0), encArg(z1)), f))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCODE_APP(h, f) -> c(APP(h, f))
   ENCODE_APP(true, f) -> c(APP(true, f))
   ENCODE_APP(map, f) -> c(APP(map, f))
   ENCODE_APP(false, f) -> c(APP(false, f))
   ENCODE_APP(filter, f) -> c(APP(filter, f))
   ENCODE_APP(cons, f) -> c(APP(cons, f))
   ENCODE_APP(f, f) -> c(APP(f, f))
   ENCODE_APP(filter2, f) -> c(APP(filter2, f))
   ENCODE_APP(g, f) -> c(APP(g, f))
   ENCODE_APP(nil, f) -> c(APP(nil, f))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
   ENCODE_APP(cons_app(z0, z1), f) -> c(APP(app(encArg(z0), encArg(z1)), f))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) by 
   ENCODE_APP(g, map) -> c(APP(g, map))
   ENCODE_APP(h, map) -> c(APP(h, map))
   ENCODE_APP(f, map) -> c(APP(f, 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))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
   ENCODE_APP(cons_app(z0, z1), f) -> c(APP(app(encArg(z0), encArg(z1)), f))
   ENCODE_APP(g, map) -> c(APP(g, map))
   ENCODE_APP(h, map) -> c(APP(h, map))
   ENCODE_APP(f, map) -> c(APP(f, 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCODE_APP(true, map) -> c(APP(true, map))
   ENCODE_APP(g, map) -> c(APP(g, map))
   ENCODE_APP(filter2, map) -> c(APP(filter2, map))
   ENCODE_APP(cons, map) -> c(APP(cons, 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(f, map) -> c(APP(f, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(h, map) -> c(APP(h, map))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
   ENCODE_APP(cons_app(z0, z1), f) -> c(APP(app(encArg(z0), encArg(z1)), f))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
S tuples:
   APP(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by 
   ENCODE_APP(g, nil) -> c(APP(g, nil))
   ENCODE_APP(h, nil) -> c(APP(h, nil))
   ENCODE_APP(f, nil) -> c(APP(f, 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))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
   ENCODE_APP(cons_app(z0, z1), f) -> c(APP(app(encArg(z0), encArg(z1)), f))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(g, nil) -> c(APP(g, nil))
   ENCODE_APP(h, nil) -> c(APP(h, nil))
   ENCODE_APP(f, nil) -> c(APP(f, 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2


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

(145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(f, nil) -> c(APP(f, nil))
   ENCODE_APP(h, nil) -> c(APP(h, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(filter2, nil) -> c(APP(filter2, nil))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(g, nil) -> c(APP(g, nil))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(g) -> g
   encArg(h) -> h
   encArg(f) -> f
   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(g, app(h, app(g, z0))) -> app(g, z0)
   app(g, app(g, z0)) -> app(g, app(h, app(g, z0)))
   app(h, app(h, z0)) -> app(h, app(app(f, app(h, z0)), 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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   ENCARG(cons_app(f, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(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(g, x1) -> c(APP(g, encArg(x1)))
   ENCODE_APP(h, x1) -> c(APP(h, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, g))) -> c10(APP(encArg(x0), app(encArg(x1), g)), ENCARG(x0), ENCARG(cons_app(x1, g)))
   ENCARG(cons_app(x0, cons_app(x1, h))) -> c10(APP(encArg(x0), app(encArg(x1), h)), ENCARG(x0), ENCARG(cons_app(x1, h)))
   ENCARG(cons_app(x0, cons_app(x1, f))) -> c10(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(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)))) -> c10(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(g, x2))) -> c10(APP(encArg(x0), app(g, encArg(x2))), ENCARG(x0), ENCARG(cons_app(g, x2)))
   ENCARG(cons_app(x0, cons_app(h, x2))) -> c10(APP(encArg(x0), app(h, encArg(x2))), ENCARG(x0), ENCARG(cons_app(h, x2)))
   ENCARG(cons_app(x0, cons_app(f, x2))) -> c10(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(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))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(g, cons_app(x1, x2))) -> c10(APP(g, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(h, cons_app(x1, x2))) -> c10(APP(h, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(f, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, g), x2)) -> c10(APP(app(encArg(x0), g), encArg(x2)), ENCARG(cons_app(x0, g)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, h), x2)) -> c10(APP(app(encArg(x0), h), encArg(x2)), ENCARG(cons_app(x0, h)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, f), x2)) -> c10(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(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)) -> c10(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(g, x1), x2)) -> c10(APP(app(g, encArg(x1)), encArg(x2)), ENCARG(cons_app(g, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(h, x1), x2)) -> c10(APP(app(h, encArg(x1)), encArg(x2)), ENCARG(cons_app(h, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(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)) -> c10(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), g)) -> c10(APP(app(encArg(x0), encArg(x1)), g), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), h)) -> c10(APP(app(encArg(x0), encArg(x1)), h), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), f)) -> c10(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(f, x1), x2)) -> c10(ENCARG(cons_app(f, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), g) -> c(APP(app(encArg(z0), encArg(z1)), g))
   ENCODE_APP(cons_app(z0, z1), h) -> c(APP(app(encArg(z0), encArg(z1)), h))
   ENCODE_APP(cons_app(z0, z1), f) -> c(APP(app(encArg(z0), encArg(z1)), f))
   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(g, app(h, app(g, z0))) -> c22(APP(g, z0))
   APP(app(map, z0), nil) -> c25
   APP(app(filter, z0), nil) -> c27
   APP(g, app(g, z0)) -> c23(APP(g, app(h, app(g, z0))), APP(g, z0))
   APP(h, app(h, z0)) -> c24(APP(h, z0))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c26(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c29(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c30(APP(app(filter, z0), z2))
   APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)) -> c28(APP(g, app(h, app(g, z0))))
   APP(app(filter, h), app(app(cons, app(h, z0)), x2)) -> c28(APP(h, app(h, z0)))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c28(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c28(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c28(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c28(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, g), app(app(cons, app(g, z0)), x1)) -> c28(APP(g, app(g, z0)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c28(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, g)), app(app(cons, app(app(cons, app(g, z0)), x2)), x3)) -> c28(APP(app(app(app(filter2, app(app(app(app(filter2, app(g, app(h, app(g, z0)))), g), app(g, z0)), x2)), app(filter, g)), app(app(cons, app(g, z0)), x2)), x3), APP(app(filter, g), app(app(cons, app(g, z0)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c28(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)) -> c28(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, g)), app(app(cons, app(app(cons, app(h, app(g, z0))), x2)), x3)) -> c28(APP(app(filter, g), app(app(cons, app(h, app(g, z0))), x2)))
   APP(app(filter, app(filter, h)), app(app(cons, app(app(cons, app(h, z0)), x2)), x3)) -> c28(APP(app(filter, h), app(app(cons, app(h, z0)), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(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)) -> c28(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c28(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:   c22_1, c25, c27, c23_2, c24_1, c26_2, c29_1, c30_1, c10_1, c28_1, c_1, c10_3, c10_2, c28_2