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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 207 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 2594 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms]
        (26) CpxRNTS
    (27) CompletionProof [UPPER BOUND(ID), 0 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) NarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
        (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (32) CpxRNTS
        (33) SimplificationProof [BOTH BOUNDS(ID, 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), 0 ms]
    (56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms]
    (98) CdtProblem
    (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (118) CdtProblem
    (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (130) CdtProblem
    (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
    (134) CdtProblem
    (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtRewritingProof [BOTH BOUNDS(ID, ID), 57 ms]
    (138) CdtProblem
    (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtRewritingProof [BOTH BOUNDS(ID, ID), 45 ms]
    (142) CdtProblem
    (143) CdtRewritingProof [BOTH BOUNDS(ID, ID), 10 ms]
    (144) CdtProblem


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

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


The TRS R consists of the following rules:

   app(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
   app(app(app(consif, false), x), ys) -> ys
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))

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

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

   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil


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

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


The TRS R consists of the following rules:

   app(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
   app(app(app(consif, false), x), ys) -> ys
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))

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

   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil

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

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

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


The TRS R consists of the following rules:

   app(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
   app(app(app(consif, false), x), ys) -> ys
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))

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

   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil

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

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

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


The TRS R consists of the following rules:

   app(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
   app(app(app(consif, false), x), ys) -> ys
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))

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

   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil

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

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

(8)
Obligation:
Innermost TRS:
Rules:
app(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
app(app(app(consif, false), x), ys) -> ys
app(app(filter, f), nil) -> nil
app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))
encArg(consif) -> consif
encArg(true) -> true
encArg(cons) -> cons
encArg(false) -> false
encArg(filter) -> filter
encArg(nil) -> nil
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_consif -> consif
encode_true -> true
encode_cons -> cons
encode_false -> false
encode_filter -> filter
encode_nil -> nil

Types:
app :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
consif :: consif:true:cons:false:filter:nil:cons_app
true :: consif:true:cons:false:filter:nil:cons_app
cons :: consif:true:cons:false:filter:nil:cons_app
false :: consif:true:cons:false:filter:nil:cons_app
filter :: consif:true:cons:false:filter:nil:cons_app
nil :: consif:true:cons:false:filter:nil:cons_app
encArg :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
cons_app :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
encode_app :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
encode_consif :: consif:true:cons:false:filter:nil:cons_app
encode_true :: consif:true:cons:false:filter:nil:cons_app
encode_cons :: consif:true:cons:false:filter:nil:cons_app
encode_false :: consif:true:cons:false:filter:nil:cons_app
encode_filter :: consif:true:cons:false:filter:nil:cons_app
encode_nil :: consif:true:cons:false:filter:nil:cons_app
hole_consif:true:cons:false:filter:nil:cons_app1_0 :: consif:true:cons:false:filter:nil:cons_app
gen_consif:true:cons:false:filter:nil:cons_app2_0 :: Nat -> consif:true:cons:false:filter:nil:cons_app

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

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

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

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

(10)
Obligation:
Innermost TRS:
Rules:
app(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
app(app(app(consif, false), x), ys) -> ys
app(app(filter, f), nil) -> nil
app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))
encArg(consif) -> consif
encArg(true) -> true
encArg(cons) -> cons
encArg(false) -> false
encArg(filter) -> filter
encArg(nil) -> nil
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_consif -> consif
encode_true -> true
encode_cons -> cons
encode_false -> false
encode_filter -> filter
encode_nil -> nil

Types:
app :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
consif :: consif:true:cons:false:filter:nil:cons_app
true :: consif:true:cons:false:filter:nil:cons_app
cons :: consif:true:cons:false:filter:nil:cons_app
false :: consif:true:cons:false:filter:nil:cons_app
filter :: consif:true:cons:false:filter:nil:cons_app
nil :: consif:true:cons:false:filter:nil:cons_app
encArg :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
cons_app :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
encode_app :: consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app -> consif:true:cons:false:filter:nil:cons_app
encode_consif :: consif:true:cons:false:filter:nil:cons_app
encode_true :: consif:true:cons:false:filter:nil:cons_app
encode_cons :: consif:true:cons:false:filter:nil:cons_app
encode_false :: consif:true:cons:false:filter:nil:cons_app
encode_filter :: consif:true:cons:false:filter:nil:cons_app
encode_nil :: consif:true:cons:false:filter:nil:cons_app
hole_consif:true:cons:false:filter:nil:cons_app1_0 :: consif:true:cons:false:filter:nil:cons_app
gen_consif:true:cons:false:filter:nil:cons_app2_0 :: Nat -> consif:true:cons:false:filter:nil:cons_app


Generator Equations:
gen_consif:true:cons:false:filter:nil:cons_app2_0(0) <=> consif
gen_consif:true:cons:false:filter:nil:cons_app2_0(+(x, 1)) <=> cons_app(consif, gen_consif:true:cons:false:filter:nil: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_consif:true:cons:false:filter:nil:cons_app2_0(n60_0)) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_consif:true:cons:false:filter:nil:cons_app2_0(0))

Induction Step:
encArg(gen_consif:true:cons:false:filter:nil:cons_app2_0(+(n60_0, 1))) ->_R^Omega(0)
app(encArg(consif), encArg(gen_consif:true:cons:false:filter:nil:cons_app2_0(n60_0))) ->_R^Omega(0)
app(consif, encArg(gen_consif:true:cons:false:filter:nil:cons_app2_0(n60_0))) ->_IH
app(consif, *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(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
   app(app(app(consif, false), x), ys) -> ys
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))

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

   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil

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(app(app(consif, true), x), ys) -> app(app(cons, x), ys)
   app(app(app(consif, false), x), ys) -> ys
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil

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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))
   app(c_app(c_app(consif, false), x), ys) -> ys
   app(c_app(filter, f), nil) -> nil
   app(c_app(c_app(consif, true), x), ys) -> app(app(cons, x), ys)

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

   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil
   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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs)) [1]
   app(c_app(c_app(consif, false), x), ys) -> ys [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(consif, true), x), ys) -> app(app(cons, x), ys) [1]
   encArg(consif) -> consif [0]
   encArg(true) -> true [0]
   encArg(cons) -> cons [0]
   encArg(false) -> false [0]
   encArg(filter) -> filter [0]
   encArg(nil) -> nil [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_consif -> consif [0]
   encode_true -> true [0]
   encode_cons -> cons [0]
   encode_false -> false [0]
   encode_filter -> filter [0]
   encode_nil -> nil [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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs)) [1]
   app(c_app(c_app(consif, false), x), ys) -> ys [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(consif, true), x), ys) -> app(app(cons, x), ys) [1]
   encArg(consif) -> consif [0]
   encArg(true) -> true [0]
   encArg(cons) -> cons [0]
   encArg(false) -> false [0]
   encArg(filter) -> filter [0]
   encArg(nil) -> nil [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_consif -> consif [0]
   encode_true -> true [0]
   encode_cons -> cons [0]
   encode_false -> false [0]
   encode_filter -> filter [0]
   encode_nil -> nil [0]
   app(x0, x1) -> c_app(x0, x1) [0]

The TRS has the following type information:
app :: filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app
c_app :: filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app
filter :: filter:c_app:cons:consif:false:nil:true:cons_app
cons :: filter:c_app:cons:consif:false:nil:true:cons_app
consif :: filter:c_app:cons:consif:false:nil:true:cons_app
false :: filter:c_app:cons:consif:false:nil:true:cons_app
nil :: filter:c_app:cons:consif:false:nil:true:cons_app
true :: filter:c_app:cons:consif:false:nil:true:cons_app
encArg :: filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app
cons_app :: filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app
encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app -> filter:c_app:cons:consif:false:nil:true:cons_app
encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app
encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app
encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app
encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app
encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app
encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app

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

(23) 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_consif -> null_encode_consif [0]
   encode_true -> null_encode_true [0]
   encode_cons -> null_encode_cons [0]
   encode_false -> null_encode_false [0]
   encode_filter -> null_encode_filter [0]
   encode_nil -> null_encode_nil [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_consif, null_encode_true, null_encode_cons, null_encode_false, null_encode_filter, null_encode_nil, null_app

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

(24)
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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs)) [1]
   app(c_app(c_app(consif, false), x), ys) -> ys [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(consif, true), x), ys) -> app(app(cons, x), ys) [1]
   encArg(consif) -> consif [0]
   encArg(true) -> true [0]
   encArg(cons) -> cons [0]
   encArg(false) -> false [0]
   encArg(filter) -> filter [0]
   encArg(nil) -> nil [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_consif -> consif [0]
   encode_true -> true [0]
   encode_cons -> cons [0]
   encode_false -> false [0]
   encode_filter -> filter [0]
   encode_nil -> nil [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_consif -> null_encode_consif [0]
   encode_true -> null_encode_true [0]
   encode_cons -> null_encode_cons [0]
   encode_false -> null_encode_false [0]
   encode_filter -> null_encode_filter [0]
   encode_nil -> null_encode_nil [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
c_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encArg :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
cons_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encArg :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app

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

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

   filter => 3
   cons => 0
   consif => 1
   false => 2
   nil => 4
   true => 5
   null_encArg => 0
   null_encode_app => 0
   null_encode_consif => 0
   null_encode_true => 0
   null_encode_cons => 0
   null_encode_false => 0
   null_encode_filter => 0
   null_encode_nil => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> ys :|: z' = ys, z = 1 + (1 + 1 + 2) + x, ys >= 0, x >= 0
   app(z, z') -{ 1 }-> app(app(app(1, app(f, x)), x), app(app(3, f), xs)) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, x), ys) :|: z' = ys, ys >= 0, x >= 0, z = 1 + (1 + 1 + 5) + x
   app(z, z') -{ 1 }-> 4 :|: z = 1 + 3 + f, f >= 0, z' = 4
   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 }-> 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_consif -{ 0 }-> 1 :|: 
   encode_consif -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 4 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 5 :|: 
   encode_true -{ 0 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.

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

(27) 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_consif
   encode_true
   encode_cons
   encode_false
   encode_filter
   encode_nil
   app_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_consif -> null_encode_consif [0]
   encode_true -> null_encode_true [0]
   encode_cons -> null_encode_cons [0]
   encode_false -> null_encode_false [0]
   encode_filter -> null_encode_filter [0]
   encode_nil -> null_encode_nil [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_consif, null_encode_true, null_encode_cons, null_encode_false, null_encode_filter, null_encode_nil, null_app

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

(28)
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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(f, x)), x), app(app(filter, f), xs)) [1]
   app(c_app(c_app(consif, false), x), ys) -> ys [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(consif, true), x), ys) -> app(app(cons, x), ys) [1]
   encArg(consif) -> consif [0]
   encArg(true) -> true [0]
   encArg(cons) -> cons [0]
   encArg(false) -> false [0]
   encArg(filter) -> filter [0]
   encArg(nil) -> nil [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_consif -> consif [0]
   encode_true -> true [0]
   encode_cons -> cons [0]
   encode_false -> false [0]
   encode_filter -> filter [0]
   encode_nil -> nil [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_consif -> null_encode_consif [0]
   encode_true -> null_encode_true [0]
   encode_cons -> null_encode_cons [0]
   encode_false -> null_encode_false [0]
   encode_filter -> null_encode_filter [0]
   encode_nil -> null_encode_nil [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
c_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encArg :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
cons_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encArg :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app

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

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

(30)
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(filter, c_app(filter, f')), c_app(c_app(cons, c_app(c_app(cons, x'), xs')), xs)) -> app(app(app(consif, app(app(app(consif, app(f', x')), x'), app(app(filter, f'), xs'))), c_app(c_app(cons, x'), xs')), app(c_app(filter, c_app(filter, f')), xs)) [2]
   app(c_app(filter, c_app(filter, f')), c_app(c_app(cons, c_app(c_app(cons, x'), xs')), xs)) -> app(app(app(consif, app(app(app(consif, app(f', x')), x'), app(app(filter, f'), xs'))), c_app(c_app(cons, x'), xs')), app(null_app, xs)) [2]
   app(c_app(filter, c_app(c_app(consif, false), x'')), c_app(c_app(cons, x), xs)) -> app(app(app(consif, x), x), app(c_app(filter, c_app(c_app(consif, false), x'')), xs)) [2]
   app(c_app(filter, c_app(c_app(consif, false), x'')), c_app(c_app(cons, x), xs)) -> app(app(app(consif, x), x), app(null_app, xs)) [2]
   app(c_app(filter, c_app(filter, f'')), c_app(c_app(cons, nil), xs)) -> app(app(app(consif, nil), nil), app(c_app(filter, c_app(filter, f'')), xs)) [2]
   app(c_app(filter, c_app(filter, f'')), c_app(c_app(cons, nil), xs)) -> app(app(app(consif, nil), nil), app(null_app, xs)) [2]
   app(c_app(filter, c_app(c_app(consif, true), x2)), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(app(cons, x2), x)), x), app(c_app(filter, c_app(c_app(consif, true), x2)), xs)) [2]
   app(c_app(filter, c_app(c_app(consif, true), x2)), c_app(c_app(cons, x), xs)) -> app(app(app(consif, app(app(cons, x2), x)), x), app(null_app, xs)) [2]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, c_app(f, x)), x), app(c_app(filter, f), xs)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, c_app(f, x)), x), app(null_app, xs)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, null_app), x), app(c_app(filter, f), xs)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(consif, null_app), x), app(null_app, xs)) [1]
   app(c_app(c_app(consif, false), x), ys) -> ys [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(consif, true), x), ys) -> app(c_app(cons, x), ys) [1]
   app(c_app(c_app(consif, true), x), ys) -> app(null_app, ys) [1]
   encArg(consif) -> consif [0]
   encArg(true) -> true [0]
   encArg(cons) -> cons [0]
   encArg(false) -> false [0]
   encArg(filter) -> filter [0]
   encArg(nil) -> nil [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_consif -> consif [0]
   encode_true -> true [0]
   encode_cons -> cons [0]
   encode_false -> false [0]
   encode_filter -> filter [0]
   encode_nil -> nil [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_consif -> null_encode_consif [0]
   encode_true -> null_encode_true [0]
   encode_cons -> null_encode_cons [0]
   encode_false -> null_encode_false [0]
   encode_filter -> null_encode_filter [0]
   encode_nil -> null_encode_nil [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
c_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encArg :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
cons_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app -> filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encArg :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_consif :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_true :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_cons :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_false :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_filter :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_encode_nil :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app
null_app :: filter:c_app:cons:consif:false:nil:true:cons_app:null_encArg:null_encode_app:null_encode_consif:null_encode_true:null_encode_cons:null_encode_false:null_encode_filter:null_encode_nil:null_app

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

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

   filter => 3
   cons => 0
   consif => 1
   false => 2
   nil => 4
   true => 5
   null_encArg => 0
   null_encode_app => 0
   null_encode_consif => 0
   null_encode_true => 0
   null_encode_cons => 0
   null_encode_false => 0
   null_encode_filter => 0
   null_encode_nil => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> ys :|: z' = ys, z = 1 + (1 + 1 + 2) + x, ys >= 0, x >= 0
   app(z, z') -{ 2 }-> app(app(app(1, x), x), app(0, xs)) :|: xs >= 0, x >= 0, z = 1 + 3 + (1 + (1 + 1 + 2) + x''), x'' >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, x), x), app(1 + 3 + (1 + (1 + 1 + 2) + x''), xs)) :|: xs >= 0, x >= 0, z = 1 + 3 + (1 + (1 + 1 + 2) + x''), x'' >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(app(1, app(f', x')), x'), app(app(3, f'), xs'))), 1 + (1 + 0 + x') + xs'), app(0, xs)) :|: xs >= 0, f' >= 0, z = 1 + 3 + (1 + 3 + f'), x' >= 0, xs' >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x') + xs')) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(app(1, app(f', x')), x'), app(app(3, f'), xs'))), 1 + (1 + 0 + x') + xs'), app(1 + 3 + (1 + 3 + f'), xs)) :|: xs >= 0, f' >= 0, z = 1 + 3 + (1 + 3 + f'), x' >= 0, xs' >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x') + xs')) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(0, x2), x)), x), app(0, xs)) :|: xs >= 0, z = 1 + 3 + (1 + (1 + 1 + 5) + x2), x >= 0, x2 >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(0, x2), x)), x), app(1 + 3 + (1 + (1 + 1 + 5) + x2), xs)) :|: xs >= 0, z = 1 + 3 + (1 + (1 + 1 + 5) + x2), x >= 0, x2 >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, 4), 4), app(0, xs)) :|: xs >= 0, f'' >= 0, z = 1 + 3 + (1 + 3 + f''), z' = 1 + (1 + 0 + 4) + xs
   app(z, z') -{ 2 }-> app(app(app(1, 4), 4), app(1 + 3 + (1 + 3 + f''), xs)) :|: xs >= 0, f'' >= 0, z = 1 + 3 + (1 + 3 + f''), z' = 1 + (1 + 0 + 4) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 0), x), app(0, xs)) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 0), x), app(1 + 3 + f, xs)) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 1 + f + x), x), app(0, xs)) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 1 + f + x), x), app(1 + 3 + f, xs)) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(0, ys) :|: z' = ys, ys >= 0, x >= 0, z = 1 + (1 + 1 + 5) + x
   app(z, z') -{ 1 }-> app(1 + 0 + x, ys) :|: z' = ys, ys >= 0, x >= 0, z = 1 + (1 + 1 + 5) + x
   app(z, z') -{ 1 }-> 4 :|: z = 1 + 3 + f, f >= 0, z' = 4
   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 }-> 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_consif -{ 0 }-> 1 :|: 
   encode_consif -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 4 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 5 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

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

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

   app(z, z') -{ 1 }-> z' :|: z' >= 0, z - 5 >= 0
   app(z, z') -{ 2 }-> app(app(app(1, x), x), app(0, xs)) :|: xs >= 0, x >= 0, z - 9 >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, x), x), app(1 + 3 + (1 + (1 + 1 + 2) + (z - 9)), xs)) :|: xs >= 0, x >= 0, z - 9 >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(app(1, app(z - 8, x')), x'), app(app(3, z - 8), xs'))), 1 + (1 + 0 + x') + xs'), app(0, xs)) :|: xs >= 0, z - 8 >= 0, x' >= 0, xs' >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x') + xs')) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(app(1, app(z - 8, x')), x'), app(app(3, z - 8), xs'))), 1 + (1 + 0 + x') + xs'), app(1 + 3 + (1 + 3 + (z - 8)), xs)) :|: xs >= 0, z - 8 >= 0, x' >= 0, xs' >= 0, z' = 1 + (1 + 0 + (1 + (1 + 0 + x') + xs')) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(0, z - 12), x)), x), app(0, xs)) :|: xs >= 0, x >= 0, z - 12 >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, app(app(0, z - 12), x)), x), app(1 + 3 + (1 + (1 + 1 + 5) + (z - 12)), xs)) :|: xs >= 0, x >= 0, z - 12 >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(1, 4), 4), app(0, z' - 6)) :|: z' - 6 >= 0, z - 8 >= 0
   app(z, z') -{ 2 }-> app(app(app(1, 4), 4), app(1 + 3 + (1 + 3 + (z - 8)), z' - 6)) :|: z' - 6 >= 0, z - 8 >= 0
   app(z, z') -{ 1 }-> app(app(app(1, 0), x), app(0, xs)) :|: z - 4 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 0), x), app(1 + 3 + (z - 4), xs)) :|: z - 4 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 1 + (z - 4) + x), x), app(0, xs)) :|: z - 4 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(1, 1 + (z - 4) + x), x), app(1 + 3 + (z - 4), xs)) :|: z - 4 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 0 + x) + xs
   app(z, z') -{ 1 }-> app(0, z') :|: z' >= 0, z - 8 >= 0
   app(z, z') -{ 1 }-> app(1 + 0 + (z - 8), z') :|: z' >= 0, z - 8 >= 0
   app(z, z') -{ 1 }-> 4 :|: z - 4 >= 0, z' = 4
   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 }-> 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_consif -{ 0 }-> 1 :|: 
   encode_consif -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 4 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 5 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   ENCARG(consif) -> c
   ENCARG(true) -> c1
   ENCARG(cons) -> c2
   ENCARG(false) -> c3
   ENCARG(filter) -> c4
   ENCARG(nil) -> c5
   ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c7(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_CONSIF -> c8
   ENCODE_TRUE -> c9
   ENCODE_CONS -> c10
   ENCODE_FALSE -> c11
   ENCODE_FILTER -> c12
   ENCODE_NIL -> c13
   APP(app(app(consif, true), z0), z1) -> c14(APP(app(cons, z0), z1), APP(cons, z0))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(app(consif, app(z0, z1)), z1), APP(consif, app(z0, z1)), APP(z0, z1), APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(app(consif, true), z0), z1) -> c14(APP(app(cons, z0), z1), APP(cons, z0))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(app(consif, app(z0, z1)), z1), APP(consif, app(z0, z1)), APP(z0, z1), APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_consif, encode_true, encode_cons, encode_false, encode_filter, encode_nil

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_CONSIF, ENCODE_TRUE, ENCODE_CONS, ENCODE_FALSE, ENCODE_FILTER, ENCODE_NIL, APP_2

Compound Symbols:   c, c1, c2, c3, c4, c5, c6_3, c7_3, c8, c9, c10, c11, c12, c13, c14_2, c15, c16, c17_6


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

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_CONS -> c10
   ENCARG(nil) -> c5
   ENCARG(false) -> c3
   ENCODE_FILTER -> c12
   ENCODE_FALSE -> c11
   ENCODE_NIL -> c13
   ENCARG(true) -> c1
   ENCARG(filter) -> c4
   ENCODE_TRUE -> c9
   ENCARG(cons) -> c2
   ENCARG(consif) -> c
   ENCODE_CONSIF -> c8

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c7(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(app(consif, true), z0), z1) -> c14(APP(app(cons, z0), z1), APP(cons, z0))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(app(consif, app(z0, z1)), z1), APP(consif, app(z0, z1)), APP(z0, z1), APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(app(consif, true), z0), z1) -> c14(APP(app(cons, z0), z1), APP(cons, z0))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(app(consif, app(z0, z1)), z1), APP(consif, app(z0, z1)), APP(z0, z1), APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_consif, encode_true, encode_cons, encode_false, encode_filter, encode_nil

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c6_3, c7_3, c14_2, c15, c16, c17_6


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c7(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_consif, encode_true, encode_cons, encode_false, encode_filter, encode_nil

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c6_3, c7_3, c15, c16, c14, c17_3


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCODE_APP(z0, z1) -> c(ENCARG(z0))
   ENCODE_APP(z0, z1) -> c(ENCARG(z1))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_consif, encode_true, encode_cons, encode_false, encode_filter, encode_nil

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c6_3, c15, c16, c14, c17_3, 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(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_consif, encode_true, encode_cons, encode_false, encode_filter, encode_nil

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c6_3, c15, c16, c14, c17_3, 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_consif -> consif
   encode_true -> true
   encode_cons -> cons
   encode_false -> false
   encode_filter -> filter
   encode_nil -> nil

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), 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:   c6_3, c15, c16, c14, c17_3, c_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c6(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0), ENCARG(consif))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(consif, x1)) -> c6(APP(consif, encArg(x1)), ENCARG(consif), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0), ENCARG(consif))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(consif, x1)) -> c6(APP(consif, encArg(x1)), ENCARG(consif), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), 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:   c15, c16, c14, c17_3, c_1, c6_3


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

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), 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:   c15, c16, c14, c17_3, c_1, c6_3, c6_2, c6_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c17(APP(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2)) by 
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x2)), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x2)), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x2)), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c15, c16, c14, c_1, c6_3, c6_2, c6_1, c17_3


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

(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c15, c16, c14, c_1, c6_3, c6_2, c6_1, c17_3, c17_2


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(consif, x1) -> c(APP(consif, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, 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(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(consif, x1) -> c(APP(consif, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_3, c6_2, c6_1, c17_3, c17_2, c_1


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(consif, x1) -> c(APP(consif, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_3, c6_2, c6_1, c17_3, c17_2, c_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c6(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(APP(consif, app(encArg(x1), encArg(x2))), ENCARG(consif), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c6(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(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(APP(consif, app(encArg(x1), encArg(x2))), ENCARG(consif), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_3, c6_2, c6_1, c17_3, c17_2, c_1


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

(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing tuple parts
----------------------------------------

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_3, c6_2, c6_1, c17_3, c17_2, c_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c6(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)), ENCARG(consif))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c6(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, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(consif, x1), x2)) -> c6(APP(app(consif, encArg(x1)), encArg(x2)), ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c6(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c6(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(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)), ENCARG(consif))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(consif, x1), x2)) -> c6(APP(app(consif, encArg(x1)), encArg(x2)), ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c6(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c6(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing tuple parts
----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, consif)) -> c6(APP(encArg(x0), consif), ENCARG(x0)) by 
   ENCARG(cons_app(consif, consif)) -> c6(APP(consif, consif), ENCARG(consif))
   ENCARG(cons_app(true, consif)) -> c6(APP(true, consif), ENCARG(true))
   ENCARG(cons_app(cons, consif)) -> c6(APP(cons, consif), ENCARG(cons))
   ENCARG(cons_app(false, consif)) -> c6(APP(false, consif), ENCARG(false))
   ENCARG(cons_app(filter, consif)) -> c6(APP(filter, consif), ENCARG(filter))
   ENCARG(cons_app(nil, consif)) -> c6(APP(nil, consif), ENCARG(nil))
   ENCARG(cons_app(cons_app(z0, z1), consif)) -> c6(APP(app(encArg(z0), encArg(z1)), consif), ENCARG(cons_app(z0, z1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(consif, consif)) -> c6(APP(consif, consif), ENCARG(consif))
   ENCARG(cons_app(true, consif)) -> c6(APP(true, consif), ENCARG(true))
   ENCARG(cons_app(cons, consif)) -> c6(APP(cons, consif), ENCARG(cons))
   ENCARG(cons_app(false, consif)) -> c6(APP(false, consif), ENCARG(false))
   ENCARG(cons_app(filter, consif)) -> c6(APP(filter, consif), ENCARG(filter))
   ENCARG(cons_app(nil, consif)) -> c6(APP(nil, consif), ENCARG(nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCARG(cons_app(true, consif)) -> c6(APP(true, consif), ENCARG(true))
   ENCARG(cons_app(cons, consif)) -> c6(APP(cons, consif), ENCARG(cons))
   ENCARG(cons_app(false, consif)) -> c6(APP(false, consif), ENCARG(false))
   ENCARG(cons_app(nil, consif)) -> c6(APP(nil, consif), ENCARG(nil))
   ENCARG(cons_app(consif, consif)) -> c6(APP(consif, consif), ENCARG(consif))
   ENCARG(cons_app(filter, consif)) -> c6(APP(filter, consif), ENCARG(filter))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, true)) -> c6(APP(encArg(x0), true), ENCARG(x0)) by 
   ENCARG(cons_app(consif, true)) -> c6(APP(consif, true), ENCARG(consif))
   ENCARG(cons_app(true, true)) -> c6(APP(true, true), ENCARG(true))
   ENCARG(cons_app(cons, true)) -> c6(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(false, true)) -> c6(APP(false, true), ENCARG(false))
   ENCARG(cons_app(filter, true)) -> c6(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(nil, true)) -> c6(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons_app(z0, z1), true)) -> c6(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(consif, true)) -> c6(APP(consif, true), ENCARG(consif))
   ENCARG(cons_app(true, true)) -> c6(APP(true, true), ENCARG(true))
   ENCARG(cons_app(cons, true)) -> c6(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(false, true)) -> c6(APP(false, true), ENCARG(false))
   ENCARG(cons_app(filter, true)) -> c6(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(nil, true)) -> c6(APP(nil, true), ENCARG(nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCARG(cons_app(nil, true)) -> c6(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c6(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c6(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(false, true)) -> c6(APP(false, true), ENCARG(false))
   ENCARG(cons_app(true, true)) -> c6(APP(true, true), ENCARG(true))
   ENCARG(cons_app(consif, true)) -> c6(APP(consif, true), ENCARG(consif))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c6(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(consif, cons)) -> c6(APP(consif, cons), ENCARG(consif))
   ENCARG(cons_app(true, cons)) -> c6(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(cons, cons)) -> c6(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(false, cons)) -> c6(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(filter, cons)) -> c6(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(nil, cons)) -> c6(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c6(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(consif, cons)) -> c6(APP(consif, cons), ENCARG(consif))
   ENCARG(cons_app(true, cons)) -> c6(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(cons, cons)) -> c6(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(false, cons)) -> c6(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(filter, cons)) -> c6(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(nil, cons)) -> c6(APP(nil, cons), ENCARG(nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCARG(cons_app(filter, cons)) -> c6(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(false, cons)) -> c6(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(true, cons)) -> c6(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(nil, cons)) -> c6(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(consif, cons)) -> c6(APP(consif, cons), ENCARG(consif))
   ENCARG(cons_app(cons, cons)) -> c6(APP(cons, cons), ENCARG(cons))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, false)) -> c6(APP(encArg(x0), false), ENCARG(x0)) by 
   ENCARG(cons_app(consif, false)) -> c6(APP(consif, false), ENCARG(consif))
   ENCARG(cons_app(true, false)) -> c6(APP(true, false), ENCARG(true))
   ENCARG(cons_app(cons, false)) -> c6(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(false, false)) -> c6(APP(false, false), ENCARG(false))
   ENCARG(cons_app(filter, false)) -> c6(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(nil, false)) -> c6(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons_app(z0, z1), false)) -> c6(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1)))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(consif, false)) -> c6(APP(consif, false), ENCARG(consif))
   ENCARG(cons_app(true, false)) -> c6(APP(true, false), ENCARG(true))
   ENCARG(cons_app(cons, false)) -> c6(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(false, false)) -> c6(APP(false, false), ENCARG(false))
   ENCARG(cons_app(filter, false)) -> c6(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(nil, false)) -> c6(APP(nil, false), ENCARG(nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCARG(cons_app(consif, false)) -> c6(APP(consif, false), ENCARG(consif))
   ENCARG(cons_app(filter, false)) -> c6(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(cons, false)) -> c6(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(true, false)) -> c6(APP(true, false), ENCARG(true))
   ENCARG(cons_app(nil, false)) -> c6(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(false, false)) -> c6(APP(false, false), ENCARG(false))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c6(APP(encArg(x0), filter), ENCARG(x0)) by 
   ENCARG(cons_app(consif, filter)) -> c6(APP(consif, filter), ENCARG(consif))
   ENCARG(cons_app(true, filter)) -> c6(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(cons, filter)) -> c6(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(false, filter)) -> c6(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(filter, filter)) -> c6(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(nil, filter)) -> c6(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons_app(z0, z1), filter)) -> c6(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(consif, filter)) -> c6(APP(consif, filter), ENCARG(consif))
   ENCARG(cons_app(true, filter)) -> c6(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(cons, filter)) -> c6(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(false, filter)) -> c6(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(filter, filter)) -> c6(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(nil, filter)) -> c6(APP(nil, filter), ENCARG(nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCARG(cons_app(false, filter)) -> c6(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(true, filter)) -> c6(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(nil, filter)) -> c6(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(filter, filter)) -> c6(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(cons, filter)) -> c6(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(consif, filter)) -> c6(APP(consif, filter), ENCARG(consif))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_2, c6_1, c17_3, c17_2, c_1, c6_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c6(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(consif, nil)) -> c6(APP(consif, nil), ENCARG(consif))
   ENCARG(cons_app(true, nil)) -> c6(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(cons, nil)) -> c6(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(false, nil)) -> c6(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(filter, nil)) -> c6(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(nil, nil)) -> c6(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c6(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(consif, nil)) -> c6(APP(consif, nil), ENCARG(consif))
   ENCARG(cons_app(true, nil)) -> c6(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(cons, nil)) -> c6(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(false, nil)) -> c6(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(filter, nil)) -> c6(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(nil, nil)) -> c6(APP(nil, nil), ENCARG(nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCARG(cons_app(true, nil)) -> c6(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(cons, nil)) -> c6(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(false, nil)) -> c6(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(consif, nil)) -> c6(APP(consif, nil), ENCARG(consif))
   ENCARG(cons_app(filter, nil)) -> c6(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(nil, nil)) -> c6(APP(nil, nil), ENCARG(nil))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, x1), nil)) -> c17(APP(app(app(consif, app(z0, x1)), x1), nil), APP(z0, x1), APP(app(filter, z0), nil)) by 
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), nil), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, z1), z1), nil), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c17(APP(app(app(consif, nil), nil), nil), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), nil), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, z1), z1), nil), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c17(APP(app(app(consif, nil), nil), nil), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), nil), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, z1), z1), nil), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c17(APP(app(app(consif, nil), nil), nil), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1


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

(93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, z1), z1), nil), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, z1), z1), nil), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1


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

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2))) by 
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(app(consif, app(app(app(consif, true), z0), x2)), x2), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, nil), nil), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(app(consif, app(app(app(consif, true), z0), x2)), x2), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, nil), nil), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(app(consif, app(app(app(consif, true), z0), x2)), x2), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, nil), nil), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2)) by 
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(x0, x1)), x1), app(app(filter, x0), x2))), app(app(cons, x1), x2)), nil), APP(app(filter, x0), app(app(cons, x1), x2)), APP(app(filter, app(filter, x0)), nil))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c17(APP(app(app(consif, app(app(app(consif, app(x0, x1)), x1), app(app(filter, x0), x2))), app(app(cons, x1), x2)), app(app(app(consif, app(app(filter, x0), z1)), z1), app(app(filter, app(filter, x0)), z2))), APP(app(filter, x0), app(app(cons, x1), x2)), APP(app(filter, app(filter, x0)), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, true), z0))), x3)), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x2))), app(app(cons, nil), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, true), z0))), x3)), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x2))), app(app(cons, nil), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, true), z0))), x3)), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x2))), app(app(cons, nil), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, consif) -> c(APP(encArg(x0), consif)) by 
   ENCODE_APP(consif, consif) -> c(APP(consif, consif))
   ENCODE_APP(true, consif) -> c(APP(true, consif))
   ENCODE_APP(cons, consif) -> c(APP(cons, consif))
   ENCODE_APP(false, consif) -> c(APP(false, consif))
   ENCODE_APP(filter, consif) -> c(APP(filter, consif))
   ENCODE_APP(nil, consif) -> c(APP(nil, consif))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(consif, consif) -> c(APP(consif, consif))
   ENCODE_APP(true, consif) -> c(APP(true, consif))
   ENCODE_APP(cons, consif) -> c(APP(cons, consif))
   ENCODE_APP(false, consif) -> c(APP(false, consif))
   ENCODE_APP(filter, consif) -> c(APP(filter, consif))
   ENCODE_APP(nil, consif) -> c(APP(nil, consif))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(true, consif) -> c(APP(true, consif))
   ENCODE_APP(nil, consif) -> c(APP(nil, consif))
   ENCODE_APP(filter, consif) -> c(APP(filter, consif))
   ENCODE_APP(consif, consif) -> c(APP(consif, consif))
   ENCODE_APP(false, consif) -> c(APP(false, consif))
   ENCODE_APP(cons, consif) -> c(APP(cons, consif))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) by 
   ENCODE_APP(consif, true) -> c(APP(consif, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(filter, true) -> c(APP(filter, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(consif, true) -> c(APP(consif, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(filter, true) -> c(APP(filter, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(consif, true) -> c(APP(consif, true))
   ENCODE_APP(filter, true) -> c(APP(filter, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) by 
   ENCODE_APP(consif, cons) -> c(APP(consif, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(consif, cons) -> c(APP(consif, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(consif, cons) -> c(APP(consif, cons))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) by 
   ENCODE_APP(consif, false) -> c(APP(consif, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(filter, false) -> c(APP(filter, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(consif, false) -> c(APP(consif, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(filter, false) -> c(APP(filter, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(consif, false) -> c(APP(consif, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(filter, false) -> c(APP(filter, false))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) by 
   ENCODE_APP(consif, filter) -> c(APP(consif, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(consif, filter) -> c(APP(consif, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(consif, filter) -> c(APP(consif, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by 
   ENCODE_APP(consif, nil) -> c(APP(consif, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(consif, nil) -> c(APP(consif, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   ENCODE_APP(consif, nil) -> c(APP(consif, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) by 
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(consif, cons_app(x1, x2)) -> c(APP(consif, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(consif, cons_app(x1, x2)) -> c(APP(consif, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))
   ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c_1, c6_3, c6_2, c17_1, c1_1


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) by 
   ENCODE_APP(cons_app(x0, x1), consif) -> c(APP(app(encArg(x0), encArg(x1)), consif))
   ENCODE_APP(cons_app(x0, x1), true) -> c(APP(app(encArg(x0), encArg(x1)), true))
   ENCODE_APP(cons_app(x0, x1), cons) -> c(APP(app(encArg(x0), encArg(x1)), cons))
   ENCODE_APP(cons_app(x0, x1), false) -> c(APP(app(encArg(x0), encArg(x1)), false))
   ENCODE_APP(cons_app(x0, x1), filter) -> c(APP(app(encArg(x0), encArg(x1)), filter))
   ENCODE_APP(cons_app(x0, x1), nil) -> c(APP(app(encArg(x0), encArg(x1)), nil))
   ENCODE_APP(cons_app(x0, x1), cons_app(z0, z1)) -> c(APP(app(encArg(x0), encArg(x1)), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(consif, x1), x2) -> c(APP(app(consif, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(consif, x1), x2) -> c(APP(app(consif, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c6_3, c6_2, c17_1, c1_1, c_1


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

(135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(consif, x1), x2) -> c(APP(app(consif, encArg(x1)), encArg(x2)))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c6_3, c6_2, c17_1, c1_1, c_1


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

(137) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace APP(app(filter, app(app(consif, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, true), z0), x1)), x1), app(app(app(consif, app(app(cons, z0), z1)), z1), app(app(filter, app(app(consif, true), z0)), x3))), APP(app(app(consif, true), z0), x1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x3))) by APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(app(consif, app(app(cons, z0), z2)), z2), app(app(filter, app(app(consif, true), z0)), z3))), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z2), z3)))
----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(app(consif, app(app(cons, z0), z2)), z2), app(app(filter, app(app(consif, true), z0)), z3))), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z2), z3)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, app(app(cons, z0), z1)), z1), app(app(app(consif, app(app(cons, z0), z2)), z2), app(app(filter, app(app(consif, true), z0)), z3))), APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, z2), z3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c6_3, c6_2, c17_1, c1_1, c_1


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

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c6_3, c6_2, c17_1, c1_1, c_1


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

(141) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace APP(app(filter, app(app(consif, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c17(APP(app(app(consif, app(app(app(consif, false), z0), x1)), x1), app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), x1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x3))) by APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, z2), z2), app(app(filter, app(app(consif, false), z0)), z3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z2), z3)))
----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, z2), z2), app(app(filter, app(app(consif, false), z0)), z3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z2), z3)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, z2), z2), app(app(filter, app(app(consif, false), z0)), z3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z2), z3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c6_3, c6_2, c17_1, c1_1, c_1


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

(143) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, app(app(app(consif, false), z0), x2)), x2), app(app(filter, app(app(consif, false), z0)), x3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, x2), x3))) by APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, z2), z2), app(app(filter, app(app(consif, false), z0)), z3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z2), z3)))
----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(consif) -> consif
   encArg(true) -> true
   encArg(cons) -> cons
   encArg(false) -> false
   encArg(filter) -> filter
   encArg(nil) -> nil
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(app(consif, true), z0), z1) -> app(app(cons, z0), z1)
   app(app(app(consif, false), z0), z1) -> z1
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))
Tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   ENCARG(cons_app(consif, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c6(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c6(ENCARG(x1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   ENCARG(cons_app(x0, cons_app(x1, consif))) -> c6(APP(encArg(x0), app(encArg(x1), consif)), ENCARG(x0), ENCARG(cons_app(x1, consif)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c6(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c6(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c6(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c6(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c6(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c6(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(consif, x2))) -> c6(APP(encArg(x0), app(consif, encArg(x2))), ENCARG(x0), ENCARG(cons_app(consif, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c6(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c6(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c6(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c6(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c6(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c6(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))) -> c6(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(consif, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c6(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, consif), x2)) -> c6(APP(app(encArg(x0), consif), encArg(x2)), ENCARG(cons_app(x0, consif)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c6(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c6(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c6(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c6(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c6(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c6(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(filter, x1), x2)) -> c6(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)) -> c6(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), consif)) -> c6(APP(app(encArg(x0), encArg(x1)), consif), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c6(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c6(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c6(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c6(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c6(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(consif, x1), x2)) -> c6(ENCARG(cons_app(consif, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c6(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c6(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c6(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c6(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   ENCODE_APP(cons_app(z0, z1), consif) -> c(APP(app(encArg(z0), encArg(z1)), consif))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(x0, cons_app(x1, consif)) -> c(APP(encArg(x0), app(encArg(x1), consif)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))))
   ENCODE_APP(x0, cons_app(consif, x2)) -> c(APP(encArg(x0), app(consif, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons_app(x0, consif), x2) -> c(APP(app(encArg(x0), consif), encArg(x2)))
   ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2)))
   ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2)))
   ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2)))
   ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2)))
   ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2)))
   ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, z2), z2), app(app(filter, app(app(consif, false), z0)), z3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z2), z3)))
S tuples:
   APP(app(app(consif, false), z0), z1) -> c15
   APP(app(filter, z0), nil) -> c16
   APP(app(app(consif, true), z0), z1) -> c14
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2)), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), x2))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, x0), app(app(cons, x1), nil)) -> c17(APP(app(filter, x0), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, z1), z1), nil))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, false), z0), z1))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, false), z0)), nil))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(app(consif, true), z0), z1))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), nil)) -> c1(APP(app(filter, app(app(consif, true), z0)), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c1(APP(app(filter, app(filter, z0)), nil))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)))
   APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c17(APP(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, x2)), x2), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, nil), nil), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c17(APP(app(app(consif, app(app(filter, z0), x1)), x1), app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(app(consif, app(app(filter, z0), x2)), x2), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c17(APP(app(app(consif, true), z0), z1), APP(app(filter, app(app(consif, true), z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c17(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), nil)), app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(z0, x1)), x1), app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2)))), app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3))
   APP(app(filter, app(filter, app(app(consif, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, z1), z1), app(app(filter, app(app(consif, false), z0)), x2))), app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(consif, false), z0))), x3)), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, false), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c17(APP(app(app(consif, app(app(app(consif, app(app(app(consif, app(z0, z1)), z1), app(app(filter, z0), z2))), app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c17(APP(app(filter, app(filter, x0)), x3))
   APP(app(filter, app(filter, app(app(consif, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c17(APP(app(filter, app(app(consif, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(consif, true), z0))), x3))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c17(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3))
   APP(app(filter, app(app(consif, false), z0)), app(app(cons, z1), app(app(cons, z2), z3))) -> c17(APP(app(app(consif, z1), z1), app(app(app(consif, z2), z2), app(app(filter, app(app(consif, false), z0)), z3))), APP(app(app(consif, false), z0), z1), APP(app(filter, app(app(consif, false), z0)), app(app(cons, z2), z3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c15, c16, c14, c6_1, c17_3, c17_2, c6_3, c6_2, c17_1, c1_1, c_1