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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 193 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), 9228 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) NarrowingProof [BOTH BOUNDS(ID, ID), 35 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 18 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 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), 13 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtRhsSimplificationProcessorProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (112) CdtProblem
    (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms]
    (124) CdtProblem
    (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 4 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (148) CdtProblem
    (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (152) CdtProblem
    (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (156) CdtProblem
    (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (160) CdtProblem
    (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (162) CdtProblem
    (163) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (164) CdtProblem
    (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (168) CdtProblem
    (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (172) CdtProblem
    (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (176) CdtProblem
    (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (178) CdtProblem
    (179) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (180) CdtProblem
    (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) 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(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0), app(s, y)) -> 0
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))

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(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id


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

(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(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0), app(s, y)) -> 0
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))

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

   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id

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(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0), app(s, y)) -> 0
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))

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

   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id

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(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(minus, x), 0') -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0'), app(s, y)) -> 0'
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))

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

   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0') -> 0'
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0'
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id

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

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

(8)
Obligation:
Innermost TRS:
Rules:
app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(minus, x), 0') -> x
app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
app(p, app(s, x)) -> x
app(app(div, 0'), app(s, y)) -> 0'
app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
app(id, x) -> x
app(id, x) -> app(s, app(s, app(s, x)))
app(id, app(p, x)) -> app(id, app(s, app(id, x)))
encArg(map) -> map
encArg(nil) -> nil
encArg(cons) -> cons
encArg(minus) -> minus
encArg(0') -> 0'
encArg(s) -> s
encArg(p) -> p
encArg(div) -> div
encArg(id) -> id
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_map -> map
encode_nil -> nil
encode_cons -> cons
encode_minus -> minus
encode_0 -> 0'
encode_s -> s
encode_p -> p
encode_div -> div
encode_id -> id

Types:
app :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
map :: map:nil:cons:minus:0':s:p:div:id:cons_app
nil :: map:nil:cons:minus:0':s:p:div:id:cons_app
cons :: map:nil:cons:minus:0':s:p:div:id:cons_app
minus :: map:nil:cons:minus:0':s:p:div:id:cons_app
0' :: map:nil:cons:minus:0':s:p:div:id:cons_app
s :: map:nil:cons:minus:0':s:p:div:id:cons_app
p :: map:nil:cons:minus:0':s:p:div:id:cons_app
div :: map:nil:cons:minus:0':s:p:div:id:cons_app
id :: map:nil:cons:minus:0':s:p:div:id:cons_app
encArg :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
cons_app :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
encode_app :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
encode_map :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_nil :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_cons :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_minus :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_0 :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_s :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_p :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_div :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_id :: map:nil:cons:minus:0':s:p:div:id:cons_app
hole_map:nil:cons:minus:0':s:p:div:id:cons_app1_3 :: map:nil:cons:minus:0':s:p:div:id:cons_app
gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3 :: Nat -> map:nil:cons:minus:0':s:p:div:id: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(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(minus, x), 0') -> x
app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
app(p, app(s, x)) -> x
app(app(div, 0'), app(s, y)) -> 0'
app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
app(id, x) -> x
app(id, x) -> app(s, app(s, app(s, x)))
app(id, app(p, x)) -> app(id, app(s, app(id, x)))
encArg(map) -> map
encArg(nil) -> nil
encArg(cons) -> cons
encArg(minus) -> minus
encArg(0') -> 0'
encArg(s) -> s
encArg(p) -> p
encArg(div) -> div
encArg(id) -> id
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_map -> map
encode_nil -> nil
encode_cons -> cons
encode_minus -> minus
encode_0 -> 0'
encode_s -> s
encode_p -> p
encode_div -> div
encode_id -> id

Types:
app :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
map :: map:nil:cons:minus:0':s:p:div:id:cons_app
nil :: map:nil:cons:minus:0':s:p:div:id:cons_app
cons :: map:nil:cons:minus:0':s:p:div:id:cons_app
minus :: map:nil:cons:minus:0':s:p:div:id:cons_app
0' :: map:nil:cons:minus:0':s:p:div:id:cons_app
s :: map:nil:cons:minus:0':s:p:div:id:cons_app
p :: map:nil:cons:minus:0':s:p:div:id:cons_app
div :: map:nil:cons:minus:0':s:p:div:id:cons_app
id :: map:nil:cons:minus:0':s:p:div:id:cons_app
encArg :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
cons_app :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
encode_app :: map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app -> map:nil:cons:minus:0':s:p:div:id:cons_app
encode_map :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_nil :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_cons :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_minus :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_0 :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_s :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_p :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_div :: map:nil:cons:minus:0':s:p:div:id:cons_app
encode_id :: map:nil:cons:minus:0':s:p:div:id:cons_app
hole_map:nil:cons:minus:0':s:p:div:id:cons_app1_3 :: map:nil:cons:minus:0':s:p:div:id:cons_app
gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3 :: Nat -> map:nil:cons:minus:0':s:p:div:id:cons_app


Generator Equations:
gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(0) <=> map
gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(+(x, 1)) <=> cons_app(map, gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(x))


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

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

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(n3629_3)) -> *3_3, rt in Omega(0)

Induction Base:
encArg(gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(0))

Induction Step:
encArg(gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(+(n3629_3, 1))) ->_R^Omega(0)
app(encArg(map), encArg(gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(n3629_3))) ->_R^Omega(0)
app(map, encArg(gen_map:nil:cons:minus:0':s:p:div:id:cons_app2_3(n3629_3))) ->_IH
app(map, *3_3)

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(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0), app(s, y)) -> 0
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))

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

   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id

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(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0), app(s, y)) -> 0
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id

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(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(p, c_app(s, x)) -> x
   app(c_app(div, 0), c_app(s, y)) -> 0
   app(c_app(map, f), nil) -> nil
   app(id, c_app(p, x)) -> app(id, app(s, app(id, x)))
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(c_app(minus, x), 0) -> x
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))

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

   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id
   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(id, x) -> x [1]
   app(id, x) -> app(s, app(s, app(s, x))) [1]
   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(p, c_app(s, x)) -> x [1]
   app(c_app(div, 0), c_app(s, y)) -> 0 [1]
   app(c_app(map, f), nil) -> nil [1]
   app(id, c_app(p, x)) -> app(id, app(s, app(id, x))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y))) [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y))) [1]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(p) -> p [0]
   encArg(div) -> div [0]
   encArg(id) -> id [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_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_p -> p [0]
   encode_div -> div [0]
   encode_id -> id [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(id, x) -> x [1]
   app(id, x) -> app(s, app(s, app(s, x))) [1]
   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(p, c_app(s, x)) -> x [1]
   app(c_app(div, 0), c_app(s, y)) -> 0 [1]
   app(c_app(map, f), nil) -> nil [1]
   app(id, c_app(p, x)) -> app(id, app(s, app(id, x))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y))) [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y))) [1]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(p) -> p [0]
   encArg(div) -> div [0]
   encArg(id) -> id [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_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_p -> p [0]
   encode_div -> div [0]
   encode_id -> id [0]
   app(x0, x1) -> c_app(x0, x1) [0]

The TRS has the following type information:
app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
c_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
cons_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app
encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app

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

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

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

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

(c) The following functions are completely defined:

   encArg_1
   encode_app_2
   encode_map
   encode_nil
   encode_cons
   encode_minus
   encode_0
   encode_s
   encode_p
   encode_div
   encode_id
   app_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_p -> null_encode_p [0]
   encode_div -> null_encode_div [0]
   encode_id -> null_encode_id [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_map, null_encode_nil, null_encode_cons, null_encode_minus, null_encode_0, null_encode_s, null_encode_p, null_encode_div, null_encode_id, null_app

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

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

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

   app(id, x) -> x [1]
   app(id, x) -> app(s, app(s, app(s, x))) [1]
   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(p, c_app(s, x)) -> x [1]
   app(c_app(div, 0), c_app(s, y)) -> 0 [1]
   app(c_app(map, f), nil) -> nil [1]
   app(id, c_app(p, x)) -> app(id, app(s, app(id, x))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y))) [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y))) [1]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(p) -> p [0]
   encArg(div) -> div [0]
   encArg(id) -> id [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_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_p -> p [0]
   encode_div -> div [0]
   encode_id -> id [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_p -> null_encode_p [0]
   encode_div -> null_encode_div [0]
   encode_id -> null_encode_id [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
c_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
cons_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app

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

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

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

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

   app(id, x) -> x [1]
   app(id, x) -> app(s, app(s, c_app(s, x))) [1]
   app(id, x) -> app(s, app(s, null_app)) [1]
   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(p, c_app(s, x)) -> x [1]
   app(c_app(div, 0), c_app(s, y)) -> 0 [1]
   app(c_app(map, f), nil) -> nil [1]
   app(id, c_app(p, x)) -> app(id, app(s, x)) [2]
   app(id, c_app(p, x)) -> app(id, app(s, app(s, app(s, app(s, x))))) [2]
   app(id, c_app(p, c_app(p, x6))) -> app(id, app(s, app(id, app(s, app(id, x6))))) [2]
   app(id, c_app(p, x)) -> app(id, app(s, c_app(id, x))) [1]
   app(id, c_app(p, x)) -> app(id, app(s, null_app)) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), y)), c_app(s, y))) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), y)), null_app)) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), app(s, app(s, app(s, y))))), c_app(s, y))) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), app(s, app(s, app(s, y))))), null_app)) [2]
   app(c_app(div, c_app(s, x)), c_app(s, c_app(p, x7))) -> app(s, app(app(div, app(c_app(minus, x), app(id, app(s, app(id, x7))))), c_app(s, c_app(p, x7)))) [2]
   app(c_app(div, c_app(s, x)), c_app(s, c_app(p, x7))) -> app(s, app(app(div, app(c_app(minus, x), app(id, app(s, app(id, x7))))), null_app)) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), c_app(id, y))), c_app(s, y))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), c_app(id, y))), null_app)) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), null_app)), c_app(s, y))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(c_app(minus, x), null_app)), null_app)) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, y)), c_app(s, y))) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, y)), null_app)) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, app(s, app(s, app(s, y))))), c_app(s, y))) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, app(s, app(s, app(s, y))))), null_app)) [2]
   app(c_app(div, c_app(s, x)), c_app(s, c_app(p, x8))) -> app(s, app(app(div, app(null_app, app(id, app(s, app(id, x8))))), c_app(s, c_app(p, x8)))) [2]
   app(c_app(div, c_app(s, x)), c_app(s, c_app(p, x8))) -> app(s, app(app(div, app(null_app, app(id, app(s, app(id, x8))))), null_app)) [2]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, c_app(id, y))), c_app(s, y))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, c_app(id, y))), null_app)) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, null_app)), c_app(s, y))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(null_app, null_app)), null_app)) [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, c_app(s, x))), app(p, c_app(s, y))) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, c_app(s, x))), app(p, null_app)) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, null_app)), app(p, c_app(s, y))) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, null_app)), app(p, null_app)) [1]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(p) -> p [0]
   encArg(div) -> div [0]
   encArg(id) -> id [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_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_p -> p [0]
   encode_div -> div [0]
   encode_id -> id [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_p -> null_encode_p [0]
   encode_div -> null_encode_div [0]
   encode_id -> null_encode_id [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
c_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
cons_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app

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

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

   id => 3
   s => 8
   map => 4
   cons => 1
   p => 7
   div => 2
   0 => 0
   nil => 6
   minus => 5
   null_encArg => 0
   null_encode_app => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_minus => 0
   null_encode_0 => 0
   null_encode_s => 0
   null_encode_p => 0
   null_encode_div => 0
   null_encode_id => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> x :|: z = 3, z' = x, x >= 0
   app(z, z') -{ 1 }-> x :|: x >= 0, z = 7, z' = 1 + 8 + x
   app(z, z') -{ 1 }-> x :|: z = 1 + 5 + x, x >= 0, z' = 0
   app(z, z') -{ 1 }-> app(app(5, app(7, 0)), app(7, 0)) :|: x >= 0, y >= 0, z = 1 + 5 + (1 + 8 + x), z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(app(5, app(7, 0)), app(7, 1 + 8 + y)) :|: x >= 0, y >= 0, z = 1 + 5 + (1 + 8 + x), z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(app(5, app(7, 1 + 8 + x)), app(7, 0)) :|: x >= 0, y >= 0, z = 1 + 5 + (1 + 8 + x), z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(app(5, app(7, 1 + 8 + x)), app(7, 1 + 8 + y)) :|: x >= 0, y >= 0, z = 1 + 5 + (1 + 8 + x), z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(app(1, app(f, x)), app(app(4, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 4 + f, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, y)), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, y)), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(8, app(8, app(8, y))))), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(8, app(8, app(8, y))))), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(3, app(8, app(3, x8))))), 0)) :|: z' = 1 + 8 + (1 + 7 + x8), z = 1 + 2 + (1 + 8 + x), x8 >= 0, x >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(3, app(8, app(3, x8))))), 1 + 8 + (1 + 7 + x8))) :|: z' = 1 + 8 + (1 + 7 + x8), z = 1 + 2 + (1 + 8 + x), x8 >= 0, x >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 0)), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 0)), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 1 + 3 + y)), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 1 + 3 + y)), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + x, y)), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + x, y)), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + x, app(8, app(8, app(8, y))))), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + x, app(8, app(8, app(8, y))))), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + x, app(3, app(8, app(3, x7))))), 0)) :|: z = 1 + 2 + (1 + 8 + x), z' = 1 + 8 + (1 + 7 + x7), x7 >= 0, x >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + x, app(3, app(8, app(3, x7))))), 1 + 8 + (1 + 7 + x7))) :|: z = 1 + 2 + (1 + 8 + x), z' = 1 + 8 + (1 + 7 + x7), x7 >= 0, x >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + x, 0)), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + x, 0)), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + x, 1 + 3 + y)), 0)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + x, 1 + 3 + y)), 1 + 8 + y)) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(8, 0)) :|: z = 3, z' = x, x >= 0
   app(z, z') -{ 1 }-> app(8, app(8, 1 + 8 + x)) :|: z = 3, z' = x, x >= 0
   app(z, z') -{ 2 }-> app(3, app(8, x)) :|: z = 3, x >= 0, z' = 1 + 7 + x
   app(z, z') -{ 2 }-> app(3, app(8, app(8, app(8, app(8, x))))) :|: z = 3, x >= 0, z' = 1 + 7 + x
   app(z, z') -{ 2 }-> app(3, app(8, app(3, app(8, app(3, x6))))) :|: z = 3, z' = 1 + 7 + (1 + 7 + x6), x6 >= 0
   app(z, z') -{ 1 }-> app(3, app(8, 0)) :|: z = 3, x >= 0, z' = 1 + 7 + x
   app(z, z') -{ 1 }-> app(3, app(8, 1 + 3 + x)) :|: z = 3, x >= 0, z' = 1 + 7 + x
   app(z, z') -{ 1 }-> 6 :|: f >= 0, z' = 6, z = 1 + 4 + f
   app(z, z') -{ 1 }-> 0 :|: z = 1 + 2 + 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_div -{ 0 }-> 2 :|: 
   encode_div -{ 0 }-> 0 :|: 
   encode_id -{ 0 }-> 3 :|: 
   encode_id -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 4 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 5 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 6 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_p -{ 0 }-> 7 :|: 
   encode_p -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 8 :|: 
   encode_s -{ 0 }-> 0 :|: 


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

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

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

   app(z, z') -{ 1 }-> z' :|: z = 3, z' >= 0
   app(z, z') -{ 1 }-> app(app(5, app(7, 0)), app(7, 0)) :|: z - 15 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(app(5, app(7, 0)), app(7, 1 + 8 + (z' - 9))) :|: z - 15 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(app(5, app(7, 1 + 8 + (z - 15))), app(7, 0)) :|: z - 15 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(app(5, app(7, 1 + 8 + (z - 15))), app(7, 1 + 8 + (z' - 9))) :|: z - 15 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(app(1, app(z - 5, x)), app(app(4, z - 5), xs)) :|: z - 5 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(8, app(8, app(8, z' - 9))))), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(8, app(8, app(8, z' - 9))))), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(3, app(8, app(3, z' - 17))))), 0)) :|: z' - 17 >= 0, z - 12 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, app(3, app(8, app(3, z' - 17))))), 1 + 8 + (1 + 7 + (z' - 17)))) :|: z' - 17 >= 0, z - 12 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 0)), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 0)), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, z' - 9)), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(0, z' - 9)), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 1 + 3 + (z' - 9))), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(0, 1 + 3 + (z' - 9))), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + (z - 12), app(8, app(8, app(8, z' - 9))))), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + (z - 12), app(8, app(8, app(8, z' - 9))))), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + (z - 12), app(3, app(8, app(3, z' - 17))))), 0)) :|: z' - 17 >= 0, z - 12 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + (z - 12), app(3, app(8, app(3, z' - 17))))), 1 + 8 + (1 + 7 + (z' - 17)))) :|: z' - 17 >= 0, z - 12 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + (z - 12), 0)), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + (z - 12), 0)), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + (z - 12), z' - 9)), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 2 }-> app(8, app(app(2, app(1 + 5 + (z - 12), z' - 9)), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + (z - 12), 1 + 3 + (z' - 9))), 0)) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(app(2, app(1 + 5 + (z - 12), 1 + 3 + (z' - 9))), 1 + 8 + (z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0
   app(z, z') -{ 1 }-> app(8, app(8, 0)) :|: z = 3, z' >= 0
   app(z, z') -{ 1 }-> app(8, app(8, 1 + 8 + z')) :|: z = 3, z' >= 0
   app(z, z') -{ 2 }-> app(3, app(8, app(8, app(8, app(8, z' - 8))))) :|: z = 3, z' - 8 >= 0
   app(z, z') -{ 2 }-> app(3, app(8, app(3, app(8, app(3, z' - 16))))) :|: z = 3, z' - 16 >= 0
   app(z, z') -{ 1 }-> app(3, app(8, 0)) :|: z = 3, z' - 8 >= 0
   app(z, z') -{ 2 }-> app(3, app(8, z' - 8)) :|: z = 3, z' - 8 >= 0
   app(z, z') -{ 1 }-> app(3, app(8, 1 + 3 + (z' - 8))) :|: z = 3, z' - 8 >= 0
   app(z, z') -{ 1 }-> 6 :|: z - 5 >= 0, z' = 6
   app(z, z') -{ 1 }-> 0 :|: z = 1 + 2 + 0, z' - 9 >= 0
   app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   app(z, z') -{ 1 }-> z - 6 :|: z - 6 >= 0, z' = 0
   app(z, z') -{ 1 }-> z' - 9 :|: z' - 9 >= 0, z = 7
   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 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_div -{ 0 }-> 2 :|: 
   encode_div -{ 0 }-> 0 :|: 
   encode_id -{ 0 }-> 3 :|: 
   encode_id -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 4 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 5 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 6 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_p -{ 0 }-> 7 :|: 
   encode_p -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 8 :|: 
   encode_s -{ 0 }-> 0 :|: 


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

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

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_p -> null_encode_p [0]
   encode_div -> null_encode_div [0]
   encode_id -> null_encode_id [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_map, null_encode_nil, null_encode_cons, null_encode_minus, null_encode_0, null_encode_s, null_encode_p, null_encode_div, null_encode_id, null_app

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

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

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

   app(id, x) -> x [1]
   app(id, x) -> app(s, app(s, app(s, x))) [1]
   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(p, c_app(s, x)) -> x [1]
   app(c_app(div, 0), c_app(s, y)) -> 0 [1]
   app(c_app(map, f), nil) -> nil [1]
   app(id, c_app(p, x)) -> app(id, app(s, app(id, x))) [1]
   app(c_app(div, c_app(s, x)), c_app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y))) [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y))) [1]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(p) -> p [0]
   encArg(div) -> div [0]
   encArg(id) -> id [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_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_p -> p [0]
   encode_div -> div [0]
   encode_id -> id [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_p -> null_encode_p [0]
   encode_div -> null_encode_div [0]
   encode_id -> null_encode_id [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
c_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
cons_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app -> id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encArg :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_map :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_nil :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_cons :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_minus :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_0 :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_s :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_p :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_div :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_encode_id :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app
null_app :: id:s:map:c_app:cons:p:div:0:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_map:null_encode_nil:null_encode_cons:null_encode_minus:null_encode_0:null_encode_s:null_encode_p:null_encode_div:null_encode_id:null_app

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

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

   id => 3
   s => 8
   map => 4
   cons => 1
   p => 7
   div => 2
   0 => 0
   nil => 6
   minus => 5
   null_encArg => 0
   null_encode_app => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_minus => 0
   null_encode_0 => 0
   null_encode_s => 0
   null_encode_p => 0
   null_encode_div => 0
   null_encode_id => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> x :|: z = 3, z' = x, x >= 0
   app(z, z') -{ 1 }-> x :|: x >= 0, z = 7, z' = 1 + 8 + x
   app(z, z') -{ 1 }-> x :|: z = 1 + 5 + x, x >= 0, z' = 0
   app(z, z') -{ 1 }-> app(app(5, app(7, app(8, x))), app(7, app(8, y))) :|: x >= 0, y >= 0, z = 1 + 5 + (1 + 8 + x), z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(app(1, app(f, x)), app(app(4, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 4 + f, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(8, app(app(2, app(app(5, x), app(3, y))), app(8, y))) :|: z = 1 + 2 + (1 + 8 + x), x >= 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 1 }-> app(8, app(8, app(8, x))) :|: z = 3, z' = x, x >= 0
   app(z, z') -{ 1 }-> app(3, app(8, app(3, x))) :|: z = 3, x >= 0, z' = 1 + 7 + x
   app(z, z') -{ 1 }-> 6 :|: f >= 0, z' = 6, z = 1 + 4 + f
   app(z, z') -{ 1 }-> 0 :|: z = 1 + 2 + 0, y >= 0, z' = 1 + 8 + y
   app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_div -{ 0 }-> 2 :|: 
   encode_div -{ 0 }-> 0 :|: 
   encode_id -{ 0 }-> 3 :|: 
   encode_id -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 4 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 5 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 6 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_p -{ 0 }-> 7 :|: 
   encode_p -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 8 :|: 
   encode_s -{ 0 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.

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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   ENCARG(map) -> c
   ENCARG(nil) -> c1
   ENCARG(cons) -> c2
   ENCARG(minus) -> c3
   ENCARG(0) -> c4
   ENCARG(s) -> c5
   ENCARG(p) -> c6
   ENCARG(div) -> c7
   ENCARG(id) -> c8
   ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_MAP -> c11
   ENCODE_NIL -> c12
   ENCODE_CONS -> c13
   ENCODE_MINUS -> c14
   ENCODE_0 -> c15
   ENCODE_S -> c16
   ENCODE_P -> c17
   ENCODE_DIV -> c18
   ENCODE_ID -> c19
   APP(app(map, z0), nil) -> c20
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(minus, z0), 0) -> c22
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(minus, app(p, app(s, z0))), APP(p, app(s, z0)), APP(s, z0), APP(p, app(s, z1)), APP(s, z1))
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1))), APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(div, app(app(minus, z0), app(id, z1))), APP(app(minus, z0), app(id, z1)), APP(minus, z0), APP(id, z1), APP(s, z1))
   APP(id, z0) -> c27
   APP(id, z0) -> c28(APP(s, app(s, app(s, z0))), APP(s, app(s, z0)), APP(s, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(s, app(id, z0)), APP(id, z0))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(minus, z0), 0) -> c22
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(minus, app(p, app(s, z0))), APP(p, app(s, z0)), APP(s, z0), APP(p, app(s, z1)), APP(s, z1))
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1))), APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(div, app(app(minus, z0), app(id, z1))), APP(app(minus, z0), app(id, z1)), APP(minus, z0), APP(id, z1), APP(s, z1))
   APP(id, z0) -> c27
   APP(id, z0) -> c28(APP(s, app(s, app(s, z0))), APP(s, app(s, z0)), APP(s, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(s, app(id, z0)), APP(id, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_map, encode_nil, encode_cons, encode_minus, encode_0, encode_s, encode_p, encode_div, encode_id

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_MAP, ENCODE_NIL, ENCODE_CONS, ENCODE_MINUS, ENCODE_0, ENCODE_S, ENCODE_P, ENCODE_DIV, ENCODE_ID, APP_2

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7, c8, c9_3, c10_3, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21_5, c22, c23_6, c24, c25, c26_7, c27, c28_3, c29_3


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

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 18 trailing nodes:
   ENCODE_P -> c17
   ENCODE_ID -> c19
   ENCARG(div) -> c7
   ENCARG(id) -> c8
   ENCARG(nil) -> c1
   ENCARG(0) -> c4
   ENCODE_0 -> c15
   ENCARG(map) -> c
   ENCODE_S -> c16
   ENCODE_MINUS -> c14
   ENCARG(s) -> c5
   ENCODE_CONS -> c13
   ENCARG(p) -> c6
   ENCODE_DIV -> c18
   ENCODE_MAP -> c11
   ENCARG(cons) -> c2
   ENCODE_NIL -> c12
   ENCARG(minus) -> c3

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(map, z0), nil) -> c20
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(minus, z0), 0) -> c22
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(minus, app(p, app(s, z0))), APP(p, app(s, z0)), APP(s, z0), APP(p, app(s, z1)), APP(s, z1))
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1))), APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(div, app(app(minus, z0), app(id, z1))), APP(app(minus, z0), app(id, z1)), APP(minus, z0), APP(id, z1), APP(s, z1))
   APP(id, z0) -> c27
   APP(id, z0) -> c28(APP(s, app(s, app(s, z0))), APP(s, app(s, z0)), APP(s, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(s, app(id, z0)), APP(id, z0))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(minus, z0), 0) -> c22
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(minus, app(p, app(s, z0))), APP(p, app(s, z0)), APP(s, z0), APP(p, app(s, z1)), APP(s, z1))
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1))), APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(div, app(app(minus, z0), app(id, z1))), APP(app(minus, z0), app(id, z1)), APP(minus, z0), APP(id, z1), APP(s, z1))
   APP(id, z0) -> c27
   APP(id, z0) -> c28(APP(s, app(s, app(s, z0))), APP(s, app(s, z0)), APP(s, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(s, app(id, z0)), APP(id, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_map, encode_nil, encode_cons, encode_minus, encode_0, encode_s, encode_p, encode_div, encode_id

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c9_3, c10_3, c20, c21_5, c22, c23_6, c24, c25, c26_7, c27, c28_3, c29_3


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_map, encode_nil, encode_cons, encode_minus, encode_0, encode_s, encode_p, encode_div, encode_id

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c9_3, c10_3, c20, c22, c24, c25, c27, c21_2, c23_3, c26_3, c28, c29_2


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   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(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_map, encode_nil, encode_cons, encode_minus, encode_0, encode_s, encode_p, encode_div, encode_id

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c9_3, c20, c22, c24, c25, c27, c21_2, c23_3, c26_3, c28, c29_2, 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(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_map, encode_nil, encode_cons, encode_minus, encode_0, encode_s, encode_p, encode_div, encode_id

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c9_3, c20, c22, c24, c25, c27, c21_2, c23_3, c26_3, c28, c29_2, 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_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_p -> p
   encode_div -> div
   encode_id -> id

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c9_3, c20, c22, c24, c25, c27, c21_2, c23_3, c26_3, c28, c29_2, c_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0), ENCARG(s))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0), ENCARG(p))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0), ENCARG(div))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0), ENCARG(id))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(map, x1)) -> c9(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(p), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(APP(div, encArg(x1)), ENCARG(div), ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(id), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0), ENCARG(s))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0), ENCARG(p))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0), ENCARG(div))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0), ENCARG(id))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(map, x1)) -> c9(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(p), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(APP(div, encArg(x1)), ENCARG(div), ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(id), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c23_3, c26_3, c28, c29_2, c_1, c9_3


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

(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 25 trailing tuple parts
----------------------------------------

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1)))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c23_3, c26_3, c28, c29_2, c_1, c9_3, c9_2, c9_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(minus, app(s, z0)), app(s, z1)) -> c23(APP(app(minus, app(p, app(s, z0))), app(p, app(s, z1))), APP(p, app(s, z0)), APP(p, app(s, z1))) by 
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c26_3, c28, c29_2, c_1, c9_3, c9_2, c9_1, c23_3


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(div, app(s, z0)), app(s, z1)) -> c26(APP(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)), APP(app(minus, z0), app(id, z1)), APP(id, z1)) by 
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c29_2, c_1, c9_3, c9_2, c9_1, c23_3, c26_3


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(id, app(p, z0)) -> c29(APP(id, app(s, app(id, z0))), APP(id, z0)) by 
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c_1, c9_3, c9_2, c9_1, c23_3, c26_3, c29_2


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(div, x1) -> c(APP(div, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(div, x1) -> c(APP(div, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_3, c9_2, c9_1, c23_3, c26_3, c29_2, c_1


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

(59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing nodes:
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(div, x1) -> c(APP(div, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_3, c9_2, c9_1, c23_3, c26_3, c29_2, c_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c9(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(p), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(APP(div, app(encArg(x1), encArg(x2))), ENCARG(div), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(id), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(p), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(APP(div, app(encArg(x1), encArg(x2))), ENCARG(div), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(id), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c9(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(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_3, c9_2, c9_1, c23_3, c26_3, c29_2, c_1


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

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_3, c9_2, c9_1, c23_3, c26_3, c29_2, c_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c9(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)), ENCARG(p))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)), ENCARG(div))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)), ENCARG(id))
   ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c9(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, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)), ENCARG(p))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)), ENCARG(div))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)), ENCARG(id))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 13 trailing tuple parts
----------------------------------------

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, map)) -> c9(APP(encArg(x0), map), ENCARG(x0)) by 
   ENCARG(cons_app(map, map)) -> c9(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c9(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c9(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(minus, map)) -> c9(APP(minus, map), ENCARG(minus))
   ENCARG(cons_app(0, map)) -> c9(APP(0, map), ENCARG(0))
   ENCARG(cons_app(s, map)) -> c9(APP(s, map), ENCARG(s))
   ENCARG(cons_app(p, map)) -> c9(APP(p, map), ENCARG(p))
   ENCARG(cons_app(div, map)) -> c9(APP(div, map), ENCARG(div))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), map)) -> c9(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1)))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(map, map)) -> c9(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c9(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c9(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(minus, map)) -> c9(APP(minus, map), ENCARG(minus))
   ENCARG(cons_app(0, map)) -> c9(APP(0, map), ENCARG(0))
   ENCARG(cons_app(s, map)) -> c9(APP(s, map), ENCARG(s))
   ENCARG(cons_app(p, map)) -> c9(APP(p, map), ENCARG(p))
   ENCARG(cons_app(div, map)) -> c9(APP(div, map), ENCARG(div))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(map, map)) -> c9(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c9(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(div, map)) -> c9(APP(div, map), ENCARG(div))
   ENCARG(cons_app(minus, map)) -> c9(APP(minus, map), ENCARG(minus))
   ENCARG(cons_app(s, map)) -> c9(APP(s, map), ENCARG(s))
   ENCARG(cons_app(0, map)) -> c9(APP(0, map), ENCARG(0))
   ENCARG(cons_app(cons, map)) -> c9(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(p, map)) -> c9(APP(p, map), ENCARG(p))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c9(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(map, nil)) -> c9(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c9(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c9(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(minus, nil)) -> c9(APP(minus, nil), ENCARG(minus))
   ENCARG(cons_app(0, nil)) -> c9(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(s, nil)) -> c9(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(p, nil)) -> c9(APP(p, nil), ENCARG(p))
   ENCARG(cons_app(div, nil)) -> c9(APP(div, nil), ENCARG(div))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c9(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(map, nil)) -> c9(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c9(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c9(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(minus, nil)) -> c9(APP(minus, nil), ENCARG(minus))
   ENCARG(cons_app(0, nil)) -> c9(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(s, nil)) -> c9(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(p, nil)) -> c9(APP(p, nil), ENCARG(p))
   ENCARG(cons_app(div, nil)) -> c9(APP(div, nil), ENCARG(div))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(div, nil)) -> c9(APP(div, nil), ENCARG(div))
   ENCARG(cons_app(minus, nil)) -> c9(APP(minus, nil), ENCARG(minus))
   ENCARG(cons_app(s, nil)) -> c9(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(0, nil)) -> c9(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(map, nil)) -> c9(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c9(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(p, nil)) -> c9(APP(p, nil), ENCARG(p))
   ENCARG(cons_app(cons, nil)) -> c9(APP(cons, nil), ENCARG(cons))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c9(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(map, cons)) -> c9(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c9(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c9(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(minus, cons)) -> c9(APP(minus, cons), ENCARG(minus))
   ENCARG(cons_app(0, cons)) -> c9(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(s, cons)) -> c9(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(p, cons)) -> c9(APP(p, cons), ENCARG(p))
   ENCARG(cons_app(div, cons)) -> c9(APP(div, cons), ENCARG(div))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c9(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(map, cons)) -> c9(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c9(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c9(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(minus, cons)) -> c9(APP(minus, cons), ENCARG(minus))
   ENCARG(cons_app(0, cons)) -> c9(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(s, cons)) -> c9(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(p, cons)) -> c9(APP(p, cons), ENCARG(p))
   ENCARG(cons_app(div, cons)) -> c9(APP(div, cons), ENCARG(div))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(0, cons)) -> c9(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(cons, cons)) -> c9(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(nil, cons)) -> c9(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(s, cons)) -> c9(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(p, cons)) -> c9(APP(p, cons), ENCARG(p))
   ENCARG(cons_app(map, cons)) -> c9(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(div, cons)) -> c9(APP(div, cons), ENCARG(div))
   ENCARG(cons_app(minus, cons)) -> c9(APP(minus, cons), ENCARG(minus))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, minus)) -> c9(APP(encArg(x0), minus), ENCARG(x0)) by 
   ENCARG(cons_app(map, minus)) -> c9(APP(map, minus), ENCARG(map))
   ENCARG(cons_app(nil, minus)) -> c9(APP(nil, minus), ENCARG(nil))
   ENCARG(cons_app(cons, minus)) -> c9(APP(cons, minus), ENCARG(cons))
   ENCARG(cons_app(minus, minus)) -> c9(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(0, minus)) -> c9(APP(0, minus), ENCARG(0))
   ENCARG(cons_app(s, minus)) -> c9(APP(s, minus), ENCARG(s))
   ENCARG(cons_app(p, minus)) -> c9(APP(p, minus), ENCARG(p))
   ENCARG(cons_app(div, minus)) -> c9(APP(div, minus), ENCARG(div))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), minus)) -> c9(APP(app(encArg(z0), encArg(z1)), minus), ENCARG(cons_app(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(map, minus)) -> c9(APP(map, minus), ENCARG(map))
   ENCARG(cons_app(nil, minus)) -> c9(APP(nil, minus), ENCARG(nil))
   ENCARG(cons_app(cons, minus)) -> c9(APP(cons, minus), ENCARG(cons))
   ENCARG(cons_app(minus, minus)) -> c9(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(0, minus)) -> c9(APP(0, minus), ENCARG(0))
   ENCARG(cons_app(s, minus)) -> c9(APP(s, minus), ENCARG(s))
   ENCARG(cons_app(p, minus)) -> c9(APP(p, minus), ENCARG(p))
   ENCARG(cons_app(div, minus)) -> c9(APP(div, minus), ENCARG(div))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(nil, minus)) -> c9(APP(nil, minus), ENCARG(nil))
   ENCARG(cons_app(map, minus)) -> c9(APP(map, minus), ENCARG(map))
   ENCARG(cons_app(0, minus)) -> c9(APP(0, minus), ENCARG(0))
   ENCARG(cons_app(p, minus)) -> c9(APP(p, minus), ENCARG(p))
   ENCARG(cons_app(div, minus)) -> c9(APP(div, minus), ENCARG(div))
   ENCARG(cons_app(minus, minus)) -> c9(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(cons, minus)) -> c9(APP(cons, minus), ENCARG(cons))
   ENCARG(cons_app(s, minus)) -> c9(APP(s, minus), ENCARG(s))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c9(APP(encArg(x0), 0), ENCARG(x0)) by 
   ENCARG(cons_app(map, 0)) -> c9(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(nil, 0)) -> c9(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(cons, 0)) -> c9(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(minus, 0)) -> c9(APP(minus, 0), ENCARG(minus))
   ENCARG(cons_app(0, 0)) -> c9(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(s, 0)) -> c9(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(p, 0)) -> c9(APP(p, 0), ENCARG(p))
   ENCARG(cons_app(div, 0)) -> c9(APP(div, 0), ENCARG(div))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), 0)) -> c9(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1)))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(map, 0)) -> c9(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(nil, 0)) -> c9(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(cons, 0)) -> c9(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(minus, 0)) -> c9(APP(minus, 0), ENCARG(minus))
   ENCARG(cons_app(0, 0)) -> c9(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(s, 0)) -> c9(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(p, 0)) -> c9(APP(p, 0), ENCARG(p))
   ENCARG(cons_app(div, 0)) -> c9(APP(div, 0), ENCARG(div))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(map, 0)) -> c9(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(div, 0)) -> c9(APP(div, 0), ENCARG(div))
   ENCARG(cons_app(minus, 0)) -> c9(APP(minus, 0), ENCARG(minus))
   ENCARG(cons_app(nil, 0)) -> c9(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(0, 0)) -> c9(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(cons, 0)) -> c9(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(p, 0)) -> c9(APP(p, 0), ENCARG(p))
   ENCARG(cons_app(s, 0)) -> c9(APP(s, 0), ENCARG(s))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, s)) -> c9(APP(encArg(x0), s), ENCARG(x0)) by 
   ENCARG(cons_app(map, s)) -> c9(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c9(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(cons, s)) -> c9(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(minus, s)) -> c9(APP(minus, s), ENCARG(minus))
   ENCARG(cons_app(0, s)) -> c9(APP(0, s), ENCARG(0))
   ENCARG(cons_app(s, s)) -> c9(APP(s, s), ENCARG(s))
   ENCARG(cons_app(p, s)) -> c9(APP(p, s), ENCARG(p))
   ENCARG(cons_app(div, s)) -> c9(APP(div, s), ENCARG(div))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), s)) -> c9(APP(app(encArg(z0), encArg(z1)), s), ENCARG(cons_app(z0, z1)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(map, s)) -> c9(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c9(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(cons, s)) -> c9(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(minus, s)) -> c9(APP(minus, s), ENCARG(minus))
   ENCARG(cons_app(0, s)) -> c9(APP(0, s), ENCARG(0))
   ENCARG(cons_app(s, s)) -> c9(APP(s, s), ENCARG(s))
   ENCARG(cons_app(p, s)) -> c9(APP(p, s), ENCARG(p))
   ENCARG(cons_app(div, s)) -> c9(APP(div, s), ENCARG(div))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(map, s)) -> c9(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c9(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(div, s)) -> c9(APP(div, s), ENCARG(div))
   ENCARG(cons_app(minus, s)) -> c9(APP(minus, s), ENCARG(minus))
   ENCARG(cons_app(s, s)) -> c9(APP(s, s), ENCARG(s))
   ENCARG(cons_app(p, s)) -> c9(APP(p, s), ENCARG(p))
   ENCARG(cons_app(cons, s)) -> c9(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(0, s)) -> c9(APP(0, s), ENCARG(0))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0))
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, p)) -> c9(APP(encArg(x0), p), ENCARG(x0)) by 
   ENCARG(cons_app(map, p)) -> c9(APP(map, p), ENCARG(map))
   ENCARG(cons_app(nil, p)) -> c9(APP(nil, p), ENCARG(nil))
   ENCARG(cons_app(cons, p)) -> c9(APP(cons, p), ENCARG(cons))
   ENCARG(cons_app(minus, p)) -> c9(APP(minus, p), ENCARG(minus))
   ENCARG(cons_app(0, p)) -> c9(APP(0, p), ENCARG(0))
   ENCARG(cons_app(s, p)) -> c9(APP(s, p), ENCARG(s))
   ENCARG(cons_app(p, p)) -> c9(APP(p, p), ENCARG(p))
   ENCARG(cons_app(div, p)) -> c9(APP(div, p), ENCARG(div))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), p)) -> c9(APP(app(encArg(z0), encArg(z1)), p), ENCARG(cons_app(z0, z1)))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(map, p)) -> c9(APP(map, p), ENCARG(map))
   ENCARG(cons_app(nil, p)) -> c9(APP(nil, p), ENCARG(nil))
   ENCARG(cons_app(cons, p)) -> c9(APP(cons, p), ENCARG(cons))
   ENCARG(cons_app(minus, p)) -> c9(APP(minus, p), ENCARG(minus))
   ENCARG(cons_app(0, p)) -> c9(APP(0, p), ENCARG(0))
   ENCARG(cons_app(s, p)) -> c9(APP(s, p), ENCARG(s))
   ENCARG(cons_app(p, p)) -> c9(APP(p, p), ENCARG(p))
   ENCARG(cons_app(div, p)) -> c9(APP(div, p), ENCARG(div))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(map, p)) -> c9(APP(map, p), ENCARG(map))
   ENCARG(cons_app(p, p)) -> c9(APP(p, p), ENCARG(p))
   ENCARG(cons_app(cons, p)) -> c9(APP(cons, p), ENCARG(cons))
   ENCARG(cons_app(div, p)) -> c9(APP(div, p), ENCARG(div))
   ENCARG(cons_app(s, p)) -> c9(APP(s, p), ENCARG(s))
   ENCARG(cons_app(minus, p)) -> c9(APP(minus, p), ENCARG(minus))
   ENCARG(cons_app(nil, p)) -> c9(APP(nil, p), ENCARG(nil))
   ENCARG(cons_app(0, p)) -> c9(APP(0, p), ENCARG(0))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0))
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, div)) -> c9(APP(encArg(x0), div), ENCARG(x0)) by 
   ENCARG(cons_app(map, div)) -> c9(APP(map, div), ENCARG(map))
   ENCARG(cons_app(nil, div)) -> c9(APP(nil, div), ENCARG(nil))
   ENCARG(cons_app(cons, div)) -> c9(APP(cons, div), ENCARG(cons))
   ENCARG(cons_app(minus, div)) -> c9(APP(minus, div), ENCARG(minus))
   ENCARG(cons_app(0, div)) -> c9(APP(0, div), ENCARG(0))
   ENCARG(cons_app(s, div)) -> c9(APP(s, div), ENCARG(s))
   ENCARG(cons_app(p, div)) -> c9(APP(p, div), ENCARG(p))
   ENCARG(cons_app(div, div)) -> c9(APP(div, div), ENCARG(div))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), div)) -> c9(APP(app(encArg(z0), encArg(z1)), div), ENCARG(cons_app(z0, z1)))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(map, div)) -> c9(APP(map, div), ENCARG(map))
   ENCARG(cons_app(nil, div)) -> c9(APP(nil, div), ENCARG(nil))
   ENCARG(cons_app(cons, div)) -> c9(APP(cons, div), ENCARG(cons))
   ENCARG(cons_app(minus, div)) -> c9(APP(minus, div), ENCARG(minus))
   ENCARG(cons_app(0, div)) -> c9(APP(0, div), ENCARG(0))
   ENCARG(cons_app(s, div)) -> c9(APP(s, div), ENCARG(s))
   ENCARG(cons_app(p, div)) -> c9(APP(p, div), ENCARG(p))
   ENCARG(cons_app(div, div)) -> c9(APP(div, div), ENCARG(div))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(map, div)) -> c9(APP(map, div), ENCARG(map))
   ENCARG(cons_app(p, div)) -> c9(APP(p, div), ENCARG(p))
   ENCARG(cons_app(div, div)) -> c9(APP(div, div), ENCARG(div))
   ENCARG(cons_app(minus, div)) -> c9(APP(minus, div), ENCARG(minus))
   ENCARG(cons_app(cons, div)) -> c9(APP(cons, div), ENCARG(cons))
   ENCARG(cons_app(s, div)) -> c9(APP(s, div), ENCARG(s))
   ENCARG(cons_app(0, div)) -> c9(APP(0, div), ENCARG(0))
   ENCARG(cons_app(nil, div)) -> c9(APP(nil, div), ENCARG(nil))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0))
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_2, c9_1, c23_3, c26_3, c29_2, c_1, c9_3


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, id)) -> c9(APP(encArg(x0), id), ENCARG(x0)) by 
   ENCARG(cons_app(map, id)) -> c9(APP(map, id), ENCARG(map))
   ENCARG(cons_app(nil, id)) -> c9(APP(nil, id), ENCARG(nil))
   ENCARG(cons_app(cons, id)) -> c9(APP(cons, id), ENCARG(cons))
   ENCARG(cons_app(minus, id)) -> c9(APP(minus, id), ENCARG(minus))
   ENCARG(cons_app(0, id)) -> c9(APP(0, id), ENCARG(0))
   ENCARG(cons_app(s, id)) -> c9(APP(s, id), ENCARG(s))
   ENCARG(cons_app(p, id)) -> c9(APP(p, id), ENCARG(p))
   ENCARG(cons_app(div, id)) -> c9(APP(div, id), ENCARG(div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id), ENCARG(id))
   ENCARG(cons_app(cons_app(z0, z1), id)) -> c9(APP(app(encArg(z0), encArg(z1)), id), ENCARG(cons_app(z0, z1)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(map, id)) -> c9(APP(map, id), ENCARG(map))
   ENCARG(cons_app(nil, id)) -> c9(APP(nil, id), ENCARG(nil))
   ENCARG(cons_app(cons, id)) -> c9(APP(cons, id), ENCARG(cons))
   ENCARG(cons_app(minus, id)) -> c9(APP(minus, id), ENCARG(minus))
   ENCARG(cons_app(0, id)) -> c9(APP(0, id), ENCARG(0))
   ENCARG(cons_app(s, id)) -> c9(APP(s, id), ENCARG(s))
   ENCARG(cons_app(p, id)) -> c9(APP(p, id), ENCARG(p))
   ENCARG(cons_app(div, id)) -> c9(APP(div, id), ENCARG(div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c23_3, c26_3, c29_2, c_1, c9_3


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

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(s, id)) -> c9(APP(s, id), ENCARG(s))
   ENCARG(cons_app(nil, id)) -> c9(APP(nil, id), ENCARG(nil))
   ENCARG(cons_app(map, id)) -> c9(APP(map, id), ENCARG(map))
   ENCARG(cons_app(div, id)) -> c9(APP(div, id), ENCARG(div))
   ENCARG(cons_app(minus, id)) -> c9(APP(minus, id), ENCARG(minus))
   ENCARG(cons_app(0, id)) -> c9(APP(0, id), ENCARG(0))
   ENCARG(cons_app(cons, id)) -> c9(APP(cons, id), ENCARG(cons))
   ENCARG(cons_app(p, id)) -> c9(APP(p, id), ENCARG(p))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c23_3, c26_3, c29_2, c_1, c9_3


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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c23_3, c26_3, c29_2, c_1, c9_3


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(p, x1)) -> c9(APP(p, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_app(p, map)) -> c9(APP(p, map), ENCARG(map))
   ENCARG(cons_app(p, nil)) -> c9(APP(p, nil), ENCARG(nil))
   ENCARG(cons_app(p, cons)) -> c9(APP(p, cons), ENCARG(cons))
   ENCARG(cons_app(p, minus)) -> c9(APP(p, minus), ENCARG(minus))
   ENCARG(cons_app(p, 0)) -> c9(APP(p, 0), ENCARG(0))
   ENCARG(cons_app(p, s)) -> c9(APP(p, s), ENCARG(s))
   ENCARG(cons_app(p, p)) -> c9(APP(p, p), ENCARG(p))
   ENCARG(cons_app(p, div)) -> c9(APP(p, div), ENCARG(div))
   ENCARG(cons_app(p, id)) -> c9(APP(p, id), ENCARG(id))
   ENCARG(cons_app(p, cons_app(z0, z1))) -> c9(APP(p, app(encArg(z0), encArg(z1))), ENCARG(cons_app(z0, z1)))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   ENCARG(cons_app(p, map)) -> c9(APP(p, map), ENCARG(map))
   ENCARG(cons_app(p, nil)) -> c9(APP(p, nil), ENCARG(nil))
   ENCARG(cons_app(p, cons)) -> c9(APP(p, cons), ENCARG(cons))
   ENCARG(cons_app(p, minus)) -> c9(APP(p, minus), ENCARG(minus))
   ENCARG(cons_app(p, 0)) -> c9(APP(p, 0), ENCARG(0))
   ENCARG(cons_app(p, s)) -> c9(APP(p, s), ENCARG(s))
   ENCARG(cons_app(p, p)) -> c9(APP(p, p), ENCARG(p))
   ENCARG(cons_app(p, div)) -> c9(APP(p, div), ENCARG(div))
   ENCARG(cons_app(p, id)) -> c9(APP(p, id), ENCARG(id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c23_3, c26_3, c29_2, c_1, c9_3


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

(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing nodes:
   ENCARG(cons_app(p, map)) -> c9(APP(p, map), ENCARG(map))
   ENCARG(cons_app(p, div)) -> c9(APP(p, div), ENCARG(div))
   ENCARG(cons_app(p, minus)) -> c9(APP(p, minus), ENCARG(minus))
   ENCARG(cons_app(p, p)) -> c9(APP(p, p), ENCARG(p))
   ENCARG(cons_app(p, nil)) -> c9(APP(p, nil), ENCARG(nil))
   ENCARG(cons_app(p, s)) -> c9(APP(p, s), ENCARG(s))
   ENCARG(cons_app(p, 0)) -> c9(APP(p, 0), ENCARG(0))
   ENCARG(cons_app(p, cons)) -> c9(APP(p, cons), ENCARG(cons))
   ENCARG(cons_app(p, id)) -> c9(APP(p, id), ENCARG(id))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c23_3, c26_3, c29_2, c_1, c9_3


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, app(p, app(s, x0))), z0), APP(p, app(s, x0)), APP(p, app(s, z0))) by 
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c23_3, c26_3, c29_2, c_1, c9_3


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), app(p, app(s, x1))), APP(p, app(s, z0)), APP(p, app(s, x1))) by 
   APP(app(minus, app(s, x0)), app(s, z0)) -> c23(APP(app(minus, x0), z0), APP(p, app(s, x0)), APP(p, app(s, z0)))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c26_3, c29_2, c_1, c9_3, c23_3


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), z0)), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0)) by 
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c26(APP(app(minus, x0), app(id, x1)), APP(id, x1))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c26(APP(app(minus, x0), app(id, x1)), APP(id, x1))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c26(APP(app(minus, x0), app(id, x1)), APP(id, x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c26_3, c29_2, c_1, c9_3, c23_3, c26_2


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

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c26_3, c29_2, c_1, c9_3, c23_3, c1_1


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(div, app(s, x0)), app(s, z0)) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, z0))))), app(s, z0)), APP(app(minus, x0), app(id, z0)), APP(id, z0)) by 
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c26(APP(app(minus, x0), app(id, x1)), APP(id, x1))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c26(APP(app(minus, x0), app(id, x1)), APP(id, x1))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c26(APP(app(minus, x0), app(id, x1)), APP(id, x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c26_3, c29_2, c_1, c9_3, c23_3, c1_1, c26_2


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c26_3, c29_2, c_1, c9_3, c23_3, c1_1, c2_1


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, z0))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0))) by 
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c26_2


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0)))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(id, z0))))), APP(id, app(p, z0))) by 
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) by 
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(cons, map) -> c(APP(cons, map))
   ENCODE_APP(minus, map) -> c(APP(minus, map))
   ENCODE_APP(0, map) -> c(APP(0, map))
   ENCODE_APP(s, map) -> c(APP(s, map))
   ENCODE_APP(p, map) -> c(APP(p, map))
   ENCODE_APP(div, map) -> c(APP(div, map))
   ENCODE_APP(id, map) -> c(APP(id, map))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(cons, map) -> c(APP(cons, map))
   ENCODE_APP(minus, map) -> c(APP(minus, map))
   ENCODE_APP(0, map) -> c(APP(0, map))
   ENCODE_APP(s, map) -> c(APP(s, map))
   ENCODE_APP(p, map) -> c(APP(p, map))
   ENCODE_APP(div, map) -> c(APP(div, map))
   ENCODE_APP(id, map) -> c(APP(id, map))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(147) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, map) -> c(APP(id, map))
Removed 8 trailing nodes:
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(div, map) -> c(APP(div, map))
   ENCODE_APP(minus, map) -> c(APP(minus, map))
   ENCODE_APP(0, map) -> c(APP(0, map))
   ENCODE_APP(s, map) -> c(APP(s, map))
   ENCODE_APP(p, map) -> c(APP(p, map))
   ENCODE_APP(cons, map) -> c(APP(cons, map))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by 
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(minus, nil) -> c(APP(minus, nil))
   ENCODE_APP(0, nil) -> c(APP(0, nil))
   ENCODE_APP(s, nil) -> c(APP(s, nil))
   ENCODE_APP(p, nil) -> c(APP(p, nil))
   ENCODE_APP(div, nil) -> c(APP(div, nil))
   ENCODE_APP(id, nil) -> c(APP(id, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(minus, nil) -> c(APP(minus, nil))
   ENCODE_APP(0, nil) -> c(APP(0, nil))
   ENCODE_APP(s, nil) -> c(APP(s, nil))
   ENCODE_APP(p, nil) -> c(APP(p, nil))
   ENCODE_APP(div, nil) -> c(APP(div, nil))
   ENCODE_APP(id, nil) -> c(APP(id, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(151) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, nil) -> c(APP(id, nil))
Removed 8 trailing nodes:
   ENCODE_APP(s, nil) -> c(APP(s, nil))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(p, nil) -> c(APP(p, nil))
   ENCODE_APP(div, nil) -> c(APP(div, nil))
   ENCODE_APP(minus, nil) -> c(APP(minus, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(0, nil) -> c(APP(0, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) by 
   ENCODE_APP(map, cons) -> c(APP(map, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(minus, cons) -> c(APP(minus, cons))
   ENCODE_APP(0, cons) -> c(APP(0, cons))
   ENCODE_APP(s, cons) -> c(APP(s, cons))
   ENCODE_APP(p, cons) -> c(APP(p, cons))
   ENCODE_APP(div, cons) -> c(APP(div, cons))
   ENCODE_APP(id, cons) -> c(APP(id, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(map, cons) -> c(APP(map, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(minus, cons) -> c(APP(minus, cons))
   ENCODE_APP(0, cons) -> c(APP(0, cons))
   ENCODE_APP(s, cons) -> c(APP(s, cons))
   ENCODE_APP(p, cons) -> c(APP(p, cons))
   ENCODE_APP(div, cons) -> c(APP(div, cons))
   ENCODE_APP(id, cons) -> c(APP(id, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(155) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, cons) -> c(APP(id, cons))
Removed 8 trailing nodes:
   ENCODE_APP(div, cons) -> c(APP(div, cons))
   ENCODE_APP(minus, cons) -> c(APP(minus, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(p, cons) -> c(APP(p, cons))
   ENCODE_APP(s, cons) -> c(APP(s, cons))
   ENCODE_APP(0, cons) -> c(APP(0, cons))
   ENCODE_APP(map, cons) -> c(APP(map, cons))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) by 
   ENCODE_APP(map, minus) -> c(APP(map, minus))
   ENCODE_APP(nil, minus) -> c(APP(nil, minus))
   ENCODE_APP(cons, minus) -> c(APP(cons, minus))
   ENCODE_APP(minus, minus) -> c(APP(minus, minus))
   ENCODE_APP(0, minus) -> c(APP(0, minus))
   ENCODE_APP(s, minus) -> c(APP(s, minus))
   ENCODE_APP(p, minus) -> c(APP(p, minus))
   ENCODE_APP(div, minus) -> c(APP(div, minus))
   ENCODE_APP(id, minus) -> c(APP(id, minus))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(map, minus) -> c(APP(map, minus))
   ENCODE_APP(nil, minus) -> c(APP(nil, minus))
   ENCODE_APP(cons, minus) -> c(APP(cons, minus))
   ENCODE_APP(minus, minus) -> c(APP(minus, minus))
   ENCODE_APP(0, minus) -> c(APP(0, minus))
   ENCODE_APP(s, minus) -> c(APP(s, minus))
   ENCODE_APP(p, minus) -> c(APP(p, minus))
   ENCODE_APP(div, minus) -> c(APP(div, minus))
   ENCODE_APP(id, minus) -> c(APP(id, minus))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(159) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, minus) -> c(APP(id, minus))
Removed 8 trailing nodes:
   ENCODE_APP(map, minus) -> c(APP(map, minus))
   ENCODE_APP(s, minus) -> c(APP(s, minus))
   ENCODE_APP(0, minus) -> c(APP(0, minus))
   ENCODE_APP(cons, minus) -> c(APP(cons, minus))
   ENCODE_APP(div, minus) -> c(APP(div, minus))
   ENCODE_APP(minus, minus) -> c(APP(minus, minus))
   ENCODE_APP(p, minus) -> c(APP(p, minus))
   ENCODE_APP(nil, minus) -> c(APP(nil, minus))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) by 
   ENCODE_APP(map, 0) -> c(APP(map, 0))
   ENCODE_APP(nil, 0) -> c(APP(nil, 0))
   ENCODE_APP(cons, 0) -> c(APP(cons, 0))
   ENCODE_APP(minus, 0) -> c(APP(minus, 0))
   ENCODE_APP(0, 0) -> c(APP(0, 0))
   ENCODE_APP(s, 0) -> c(APP(s, 0))
   ENCODE_APP(p, 0) -> c(APP(p, 0))
   ENCODE_APP(div, 0) -> c(APP(div, 0))
   ENCODE_APP(id, 0) -> c(APP(id, 0))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(map, 0) -> c(APP(map, 0))
   ENCODE_APP(nil, 0) -> c(APP(nil, 0))
   ENCODE_APP(cons, 0) -> c(APP(cons, 0))
   ENCODE_APP(minus, 0) -> c(APP(minus, 0))
   ENCODE_APP(0, 0) -> c(APP(0, 0))
   ENCODE_APP(s, 0) -> c(APP(s, 0))
   ENCODE_APP(p, 0) -> c(APP(p, 0))
   ENCODE_APP(div, 0) -> c(APP(div, 0))
   ENCODE_APP(id, 0) -> c(APP(id, 0))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(163) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, 0) -> c(APP(id, 0))
Removed 8 trailing nodes:
   ENCODE_APP(map, 0) -> c(APP(map, 0))
   ENCODE_APP(0, 0) -> c(APP(0, 0))
   ENCODE_APP(nil, 0) -> c(APP(nil, 0))
   ENCODE_APP(cons, 0) -> c(APP(cons, 0))
   ENCODE_APP(p, 0) -> c(APP(p, 0))
   ENCODE_APP(s, 0) -> c(APP(s, 0))
   ENCODE_APP(div, 0) -> c(APP(div, 0))
   ENCODE_APP(minus, 0) -> c(APP(minus, 0))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) by 
   ENCODE_APP(map, s) -> c(APP(map, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(cons, s) -> c(APP(cons, s))
   ENCODE_APP(minus, s) -> c(APP(minus, s))
   ENCODE_APP(0, s) -> c(APP(0, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(p, s) -> c(APP(p, s))
   ENCODE_APP(div, s) -> c(APP(div, s))
   ENCODE_APP(id, s) -> c(APP(id, s))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(map, s) -> c(APP(map, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(cons, s) -> c(APP(cons, s))
   ENCODE_APP(minus, s) -> c(APP(minus, s))
   ENCODE_APP(0, s) -> c(APP(0, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(p, s) -> c(APP(p, s))
   ENCODE_APP(div, s) -> c(APP(div, s))
   ENCODE_APP(id, s) -> c(APP(id, s))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(167) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, s) -> c(APP(id, s))
Removed 8 trailing nodes:
   ENCODE_APP(div, s) -> c(APP(div, s))
   ENCODE_APP(minus, s) -> c(APP(minus, s))
   ENCODE_APP(p, s) -> c(APP(p, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(cons, s) -> c(APP(cons, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(0, s) -> c(APP(0, s))
   ENCODE_APP(map, s) -> c(APP(map, s))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, p) -> c(APP(encArg(x0), p))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, p) -> c(APP(encArg(x0), p)) by 
   ENCODE_APP(map, p) -> c(APP(map, p))
   ENCODE_APP(nil, p) -> c(APP(nil, p))
   ENCODE_APP(cons, p) -> c(APP(cons, p))
   ENCODE_APP(minus, p) -> c(APP(minus, p))
   ENCODE_APP(0, p) -> c(APP(0, p))
   ENCODE_APP(s, p) -> c(APP(s, p))
   ENCODE_APP(p, p) -> c(APP(p, p))
   ENCODE_APP(div, p) -> c(APP(div, p))
   ENCODE_APP(id, p) -> c(APP(id, p))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(map, p) -> c(APP(map, p))
   ENCODE_APP(nil, p) -> c(APP(nil, p))
   ENCODE_APP(cons, p) -> c(APP(cons, p))
   ENCODE_APP(minus, p) -> c(APP(minus, p))
   ENCODE_APP(0, p) -> c(APP(0, p))
   ENCODE_APP(s, p) -> c(APP(s, p))
   ENCODE_APP(p, p) -> c(APP(p, p))
   ENCODE_APP(div, p) -> c(APP(div, p))
   ENCODE_APP(id, p) -> c(APP(id, p))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(171) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, p) -> c(APP(id, p))
Removed 8 trailing nodes:
   ENCODE_APP(nil, p) -> c(APP(nil, p))
   ENCODE_APP(0, p) -> c(APP(0, p))
   ENCODE_APP(cons, p) -> c(APP(cons, p))
   ENCODE_APP(p, p) -> c(APP(p, p))
   ENCODE_APP(div, p) -> c(APP(div, p))
   ENCODE_APP(s, p) -> c(APP(s, p))
   ENCODE_APP(minus, p) -> c(APP(minus, p))
   ENCODE_APP(map, p) -> c(APP(map, p))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, div) -> c(APP(encArg(x0), div))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) by 
   ENCODE_APP(map, div) -> c(APP(map, div))
   ENCODE_APP(nil, div) -> c(APP(nil, div))
   ENCODE_APP(cons, div) -> c(APP(cons, div))
   ENCODE_APP(minus, div) -> c(APP(minus, div))
   ENCODE_APP(0, div) -> c(APP(0, div))
   ENCODE_APP(s, div) -> c(APP(s, div))
   ENCODE_APP(p, div) -> c(APP(p, div))
   ENCODE_APP(div, div) -> c(APP(div, div))
   ENCODE_APP(id, div) -> c(APP(id, div))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
   ENCODE_APP(map, div) -> c(APP(map, div))
   ENCODE_APP(nil, div) -> c(APP(nil, div))
   ENCODE_APP(cons, div) -> c(APP(cons, div))
   ENCODE_APP(minus, div) -> c(APP(minus, div))
   ENCODE_APP(0, div) -> c(APP(0, div))
   ENCODE_APP(s, div) -> c(APP(s, div))
   ENCODE_APP(p, div) -> c(APP(p, div))
   ENCODE_APP(div, div) -> c(APP(div, div))
   ENCODE_APP(id, div) -> c(APP(id, div))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(175) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, div) -> c(APP(id, div))
Removed 8 trailing nodes:
   ENCODE_APP(s, div) -> c(APP(s, div))
   ENCODE_APP(map, div) -> c(APP(map, div))
   ENCODE_APP(div, div) -> c(APP(div, div))
   ENCODE_APP(minus, div) -> c(APP(minus, div))
   ENCODE_APP(p, div) -> c(APP(p, div))
   ENCODE_APP(cons, div) -> c(APP(cons, div))
   ENCODE_APP(0, div) -> c(APP(0, div))
   ENCODE_APP(nil, div) -> c(APP(nil, div))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, id) -> c(APP(encArg(x0), id))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, id) -> c(APP(encArg(x0), id)) by 
   ENCODE_APP(map, id) -> c(APP(map, id))
   ENCODE_APP(nil, id) -> c(APP(nil, id))
   ENCODE_APP(cons, id) -> c(APP(cons, id))
   ENCODE_APP(minus, id) -> c(APP(minus, id))
   ENCODE_APP(0, id) -> c(APP(0, id))
   ENCODE_APP(s, id) -> c(APP(s, id))
   ENCODE_APP(p, id) -> c(APP(p, id))
   ENCODE_APP(div, id) -> c(APP(div, id))
   ENCODE_APP(id, id) -> c(APP(id, id))
   ENCODE_APP(cons_app(z0, z1), id) -> c(APP(app(encArg(z0), encArg(z1)), id))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))
   ENCODE_APP(map, id) -> c(APP(map, id))
   ENCODE_APP(nil, id) -> c(APP(nil, id))
   ENCODE_APP(cons, id) -> c(APP(cons, id))
   ENCODE_APP(minus, id) -> c(APP(minus, id))
   ENCODE_APP(0, id) -> c(APP(0, id))
   ENCODE_APP(s, id) -> c(APP(s, id))
   ENCODE_APP(p, id) -> c(APP(p, id))
   ENCODE_APP(div, id) -> c(APP(div, id))
   ENCODE_APP(id, id) -> c(APP(id, id))
   ENCODE_APP(cons_app(z0, z1), id) -> c(APP(app(encArg(z0), encArg(z1)), id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(179) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_APP(id, id) -> c(APP(id, id))
Removed 8 trailing nodes:
   ENCODE_APP(s, id) -> c(APP(s, id))
   ENCODE_APP(p, id) -> c(APP(p, id))
   ENCODE_APP(cons, id) -> c(APP(cons, id))
   ENCODE_APP(nil, id) -> c(APP(nil, id))
   ENCODE_APP(0, id) -> c(APP(0, id))
   ENCODE_APP(div, id) -> c(APP(div, id))
   ENCODE_APP(minus, id) -> c(APP(minus, id))
   ENCODE_APP(map, id) -> c(APP(map, id))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))
   ENCODE_APP(cons_app(z0, z1), id) -> c(APP(app(encArg(z0), encArg(z1)), id))
S tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(181) 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, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, minus)) -> c(APP(encArg(x0), app(encArg(x1), minus)))
   ENCODE_APP(x0, cons_app(x1, 0)) -> c(APP(encArg(x0), app(encArg(x1), 0)))
   ENCODE_APP(x0, cons_app(x1, s)) -> c(APP(encArg(x0), app(encArg(x1), s)))
   ENCODE_APP(x0, cons_app(x1, p)) -> c(APP(encArg(x0), app(encArg(x1), p)))
   ENCODE_APP(x0, cons_app(x1, div)) -> c(APP(encArg(x0), app(encArg(x1), div)))
   ENCODE_APP(x0, cons_app(x1, id)) -> c(APP(encArg(x0), app(encArg(x1), id)))
   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(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(minus, x2)) -> c(APP(encArg(x0), app(minus, encArg(x2))))
   ENCODE_APP(x0, cons_app(0, x2)) -> c(APP(encArg(x0), app(0, encArg(x2))))
   ENCODE_APP(x0, cons_app(s, x2)) -> c(APP(encArg(x0), app(s, encArg(x2))))
   ENCODE_APP(x0, cons_app(p, x2)) -> c(APP(encArg(x0), app(p, encArg(x2))))
   ENCODE_APP(x0, cons_app(div, x2)) -> c(APP(encArg(x0), app(div, encArg(x2))))
   ENCODE_APP(x0, cons_app(id, x2)) -> c(APP(encArg(x0), app(id, 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(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(minus, cons_app(x1, x2)) -> c(APP(minus, app(encArg(x1), encArg(x2))))
   ENCODE_APP(0, cons_app(x1, x2)) -> c(APP(0, app(encArg(x1), encArg(x2))))
   ENCODE_APP(s, cons_app(x1, x2)) -> c(APP(s, app(encArg(x1), encArg(x2))))
   ENCODE_APP(p, cons_app(x1, x2)) -> c(APP(p, app(encArg(x1), encArg(x2))))
   ENCODE_APP(div, cons_app(x1, x2)) -> c(APP(div, app(encArg(x1), encArg(x2))))
   ENCODE_APP(id, cons_app(x1, x2)) -> c(APP(id, 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))))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))
   ENCODE_APP(cons_app(z0, z1), id) -> c(APP(app(encArg(z0), encArg(z1)), id))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, minus)) -> c(APP(encArg(x0), app(encArg(x1), minus)))
   ENCODE_APP(x0, cons_app(x1, 0)) -> c(APP(encArg(x0), app(encArg(x1), 0)))
   ENCODE_APP(x0, cons_app(x1, s)) -> c(APP(encArg(x0), app(encArg(x1), s)))
   ENCODE_APP(x0, cons_app(x1, p)) -> c(APP(encArg(x0), app(encArg(x1), p)))
   ENCODE_APP(x0, cons_app(x1, div)) -> c(APP(encArg(x0), app(encArg(x1), div)))
   ENCODE_APP(x0, cons_app(x1, id)) -> c(APP(encArg(x0), app(encArg(x1), id)))
   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(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(minus, x2)) -> c(APP(encArg(x0), app(minus, encArg(x2))))
   ENCODE_APP(x0, cons_app(0, x2)) -> c(APP(encArg(x0), app(0, encArg(x2))))
   ENCODE_APP(x0, cons_app(s, x2)) -> c(APP(encArg(x0), app(s, encArg(x2))))
   ENCODE_APP(x0, cons_app(p, x2)) -> c(APP(encArg(x0), app(p, encArg(x2))))
   ENCODE_APP(x0, cons_app(div, x2)) -> c(APP(encArg(x0), app(div, encArg(x2))))
   ENCODE_APP(x0, cons_app(id, x2)) -> c(APP(encArg(x0), app(id, 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(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(minus, cons_app(x1, x2)) -> c(APP(minus, app(encArg(x1), encArg(x2))))
   ENCODE_APP(0, cons_app(x1, x2)) -> c(APP(0, app(encArg(x1), encArg(x2))))
   ENCODE_APP(s, cons_app(x1, x2)) -> c(APP(s, app(encArg(x1), encArg(x2))))
   ENCODE_APP(p, cons_app(x1, x2)) -> c(APP(p, app(encArg(x1), encArg(x2))))
   ENCODE_APP(div, cons_app(x1, x2)) -> c(APP(div, app(encArg(x1), encArg(x2))))
   ENCODE_APP(id, cons_app(x1, x2)) -> c(APP(id, 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(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1


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

(183) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing nodes:
   ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2))))
   ENCODE_APP(s, cons_app(x1, x2)) -> c(APP(s, app(encArg(x1), encArg(x2))))
   ENCODE_APP(div, cons_app(x1, x2)) -> c(APP(div, app(encArg(x1), encArg(x2))))
   ENCODE_APP(minus, cons_app(x1, x2)) -> c(APP(minus, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(0, cons_app(x1, x2)) -> c(APP(0, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(p) -> p
   encArg(div) -> div
   encArg(id) -> id
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))
   app(p, app(s, z0)) -> z0
   app(app(div, 0), app(s, z0)) -> 0
   app(app(div, app(s, z0)), app(s, z1)) -> app(s, app(app(div, app(app(minus, z0), app(id, z1))), app(s, z1)))
   app(id, z0) -> z0
   app(id, z0) -> app(s, app(s, app(s, z0)))
   app(id, app(p, z0)) -> app(id, app(s, app(id, z0)))
Tuples:
   APP(app(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   ENCARG(cons_app(map, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(minus, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(div, x1)) -> c9(ENCARG(x1))
   ENCARG(cons_app(id, x1)) -> c9(APP(id, encArg(x1)), ENCARG(x1))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   ENCODE_APP(p, x1) -> c(APP(p, encArg(x1)))
   ENCODE_APP(id, x1) -> c(APP(id, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c9(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c9(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c9(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c9(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c9(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c9(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, p))) -> c9(APP(encArg(x0), app(encArg(x1), p)), ENCARG(x0), ENCARG(cons_app(x1, p)))
   ENCARG(cons_app(x0, cons_app(x1, div))) -> c9(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div)))
   ENCARG(cons_app(x0, cons_app(x1, id))) -> c9(APP(encArg(x0), app(encArg(x1), id)), ENCARG(x0), ENCARG(cons_app(x1, id)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c9(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(map, x2))) -> c9(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c9(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c9(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(minus, x2))) -> c9(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c9(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c9(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(p, x2))) -> c9(APP(encArg(x0), app(p, encArg(x2))), ENCARG(x0), ENCARG(cons_app(p, x2)))
   ENCARG(cons_app(x0, cons_app(div, x2))) -> c9(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2)))
   ENCARG(cons_app(x0, cons_app(id, x2))) -> c9(APP(encArg(x0), app(id, encArg(x2))), ENCARG(x0), ENCARG(cons_app(id, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c9(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))) -> c9(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(p, cons_app(x1, x2))) -> c9(APP(p, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(div, cons_app(x1, x2))) -> c9(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(id, cons_app(x1, x2))) -> c9(APP(id, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c9(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c9(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c9(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c9(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c9(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c9(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, p), x2)) -> c9(APP(app(encArg(x0), p), encArg(x2)), ENCARG(cons_app(x0, p)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, div), x2)) -> c9(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, id), x2)) -> c9(APP(app(encArg(x0), id), encArg(x2)), ENCARG(cons_app(x0, id)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c9(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(map, x1), x2)) -> c9(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(minus, x1), x2)) -> c9(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(p, x1), x2)) -> c9(APP(app(p, encArg(x1)), encArg(x2)), ENCARG(cons_app(p, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(div, x1), x2)) -> c9(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(id, x1), x2)) -> c9(APP(app(id, encArg(x1)), encArg(x2)), ENCARG(cons_app(id, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c9(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), map)) -> c9(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c9(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c9(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c9(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c9(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c9(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), p)) -> c9(APP(app(encArg(x0), encArg(x1)), p), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), div)) -> c9(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), id)) -> c9(APP(app(encArg(x0), encArg(x1)), id), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c9(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c9(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c9(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c9(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(id, map)) -> c9(APP(id, map))
   ENCARG(cons_app(id, nil)) -> c9(APP(id, nil))
   ENCARG(cons_app(id, cons)) -> c9(APP(id, cons))
   ENCARG(cons_app(id, minus)) -> c9(APP(id, minus))
   ENCARG(cons_app(id, 0)) -> c9(APP(id, 0))
   ENCARG(cons_app(id, s)) -> c9(APP(id, s))
   ENCARG(cons_app(id, p)) -> c9(APP(id, p))
   ENCARG(cons_app(id, div)) -> c9(APP(id, div))
   ENCARG(cons_app(id, id)) -> c9(APP(id, id))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), p) -> c(APP(app(encArg(z0), encArg(z1)), p))
   ENCODE_APP(cons_app(z0, z1), div) -> c(APP(app(encArg(z0), encArg(z1)), div))
   ENCODE_APP(cons_app(z0, z1), id) -> c(APP(app(encArg(z0), encArg(z1)), id))
   ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map)))
   ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil)))
   ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons)))
   ENCODE_APP(x0, cons_app(x1, minus)) -> c(APP(encArg(x0), app(encArg(x1), minus)))
   ENCODE_APP(x0, cons_app(x1, 0)) -> c(APP(encArg(x0), app(encArg(x1), 0)))
   ENCODE_APP(x0, cons_app(x1, s)) -> c(APP(encArg(x0), app(encArg(x1), s)))
   ENCODE_APP(x0, cons_app(x1, p)) -> c(APP(encArg(x0), app(encArg(x1), p)))
   ENCODE_APP(x0, cons_app(x1, div)) -> c(APP(encArg(x0), app(encArg(x1), div)))
   ENCODE_APP(x0, cons_app(x1, id)) -> c(APP(encArg(x0), app(encArg(x1), id)))
   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(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2))))
   ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2))))
   ENCODE_APP(x0, cons_app(minus, x2)) -> c(APP(encArg(x0), app(minus, encArg(x2))))
   ENCODE_APP(x0, cons_app(0, x2)) -> c(APP(encArg(x0), app(0, encArg(x2))))
   ENCODE_APP(x0, cons_app(s, x2)) -> c(APP(encArg(x0), app(s, encArg(x2))))
   ENCODE_APP(x0, cons_app(p, x2)) -> c(APP(encArg(x0), app(p, encArg(x2))))
   ENCODE_APP(x0, cons_app(div, x2)) -> c(APP(encArg(x0), app(div, encArg(x2))))
   ENCODE_APP(x0, cons_app(id, x2)) -> c(APP(encArg(x0), app(id, 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(p, cons_app(x1, x2)) -> c(APP(p, app(encArg(x1), encArg(x2))))
   ENCODE_APP(id, cons_app(x1, x2)) -> c(APP(id, 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(map, z0), nil) -> c20
   APP(app(minus, z0), 0) -> c22
   APP(p, app(s, z0)) -> c24
   APP(app(div, 0), app(s, z0)) -> c25
   APP(id, z0) -> c27
   APP(app(map, z0), app(app(cons, z1), z2)) -> c21(APP(z0, z1), APP(app(map, z0), z2))
   APP(id, z0) -> c28
   APP(id, app(p, z0)) -> c29(APP(id, app(s, z0)), APP(id, z0))
   APP(id, app(p, z0)) -> c29(APP(id, app(s, app(s, app(s, app(s, z0))))), APP(id, z0))
   APP(app(minus, app(s, z0)), app(s, x1)) -> c23(APP(app(minus, z0), x1), APP(p, app(s, z0)), APP(p, app(s, x1)))
   APP(app(div, app(s, z0)), app(s, 0)) -> c26(APP(app(div, z0), app(s, 0)), APP(app(minus, z0), app(id, 0)), APP(id, 0))
   APP(app(div, app(s, app(s, z0))), app(s, app(s, z1))) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, z1)))), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(id, app(s, z1))), APP(id, app(s, z1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c1(APP(id, x1))
   APP(app(div, app(s, app(s, z0))), app(s, x1)) -> c26(APP(app(div, app(app(minus, app(p, app(s, z0))), app(p, app(s, app(s, app(s, x1)))))), app(s, x1)), APP(app(minus, app(s, z0)), app(id, x1)), APP(id, x1))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(app(minus, x0), app(id, x1)))
   APP(app(div, app(s, x0)), app(s, x1)) -> c2(APP(id, x1))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(id, x1)))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c26(APP(app(div, app(app(minus, x0), app(s, app(s, app(s, app(s, app(id, x1))))))), app(s, app(p, x1))), APP(app(minus, x0), app(id, app(p, x1))), APP(id, app(p, x1)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, z0)))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, z0))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(s, app(s, app(s, z0))))))), app(s, app(p, z0))), APP(app(minus, x0), app(id, app(p, z0))), APP(id, app(p, z0)))
   APP(app(div, app(s, x0)), app(s, app(p, app(p, z0)))) -> c26(APP(app(div, app(app(minus, x0), app(id, app(s, app(id, app(s, app(id, z0))))))), app(s, app(p, app(p, z0)))), APP(app(minus, x0), app(id, app(p, app(p, z0)))), APP(id, app(p, app(p, z0))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(app(minus, x0), app(id, app(p, x1))))
   APP(app(div, app(s, x0)), app(s, app(p, x1))) -> c3(APP(id, app(p, x1)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(id, x0)))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(s, app(s, app(s, app(s, app(s, app(id, x0))))))), APP(id, app(p, x0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, z0)))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, z0))) -> c29(APP(id, app(s, app(id, app(s, app(s, app(s, app(s, z0))))))), APP(id, app(p, z0)))
   APP(id, app(p, app(p, app(p, z0)))) -> c29(APP(id, app(s, app(id, app(s, app(id, app(s, app(id, z0))))))), APP(id, app(p, app(p, z0))))
   APP(id, app(p, app(p, x0))) -> c29(APP(id, app(p, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c20, c22, c24, c25, c27, c21_2, c28, c9_1, c9_2, c29_2, c_1, c9_3, c23_3, c26_3, c1_1, c2_1, c3_1, c29_1