/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 178 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), 7539 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), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 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), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(36) CdtProblem
    (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms]
    (64) CdtProblem
    (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (96) CdtProblem
    (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
    (100) CdtProblem
    (101) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 9 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 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), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
    (140) CdtProblem
    (141) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms]
    (144) CdtProblem
    (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 6 ms]
    (148) CdtProblem
    (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (150) CdtProblem
    (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms]
    (154) CdtProblem
    (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (164) CdtProblem
    (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) CdtProblem
    (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (178) CdtProblem
    (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
    (180) CdtProblem
    (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) CdtProblem
    (185) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms]
    (186) 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(and, true), true) -> true
   app(app(and, x), false) -> false
   app(app(and, false), y) -> false
   app(app(or, true), y) -> true
   app(app(or, x), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, p), nil) -> true
   app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(app(forsome, p), nil) -> false
   app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))

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

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

   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome


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

(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(and, true), true) -> true
   app(app(and, x), false) -> false
   app(app(and, false), y) -> false
   app(app(or, true), y) -> true
   app(app(or, x), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, p), nil) -> true
   app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(app(forsome, p), nil) -> false
   app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))

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

   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome

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(and, true), true) -> true
   app(app(and, x), false) -> false
   app(app(and, false), y) -> false
   app(app(or, true), y) -> true
   app(app(or, x), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, p), nil) -> true
   app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(app(forsome, p), nil) -> false
   app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))

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

   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome

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(and, true), true) -> true
   app(app(and, x), false) -> false
   app(app(and, false), y) -> false
   app(app(or, true), y) -> true
   app(app(or, x), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, p), nil) -> true
   app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(app(forsome, p), nil) -> false
   app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))

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

   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome

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

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

(8)
Obligation:
Innermost TRS:
Rules:
app(app(and, true), true) -> true
app(app(and, x), false) -> false
app(app(and, false), y) -> false
app(app(or, true), y) -> true
app(app(or, x), true) -> true
app(app(or, false), false) -> false
app(app(forall, p), nil) -> true
app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
app(app(forsome, p), nil) -> false
app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))
encArg(and) -> and
encArg(true) -> true
encArg(false) -> false
encArg(or) -> or
encArg(forall) -> forall
encArg(nil) -> nil
encArg(cons) -> cons
encArg(forsome) -> forsome
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_and -> and
encode_true -> true
encode_false -> false
encode_or -> or
encode_forall -> forall
encode_nil -> nil
encode_cons -> cons
encode_forsome -> forsome

Types:
app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
and :: and:true:false:or:forall:nil:cons:forsome:cons_app
true :: and:true:false:or:forall:nil:cons:forsome:cons_app
false :: and:true:false:or:forall:nil:cons:forsome:cons_app
or :: and:true:false:or:forall:nil:cons:forsome:cons_app
forall :: and:true:false:or:forall:nil:cons:forsome:cons_app
nil :: and:true:false:or:forall:nil:cons:forsome:cons_app
cons :: and:true:false:or:forall:nil:cons:forsome:cons_app
forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app
encArg :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
cons_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
encode_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
encode_and :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_true :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_false :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_or :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_forall :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_nil :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_cons :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app
hole_and:true:false:or:forall:nil:cons:forsome:cons_app1_0 :: and:true:false:or:forall:nil:cons:forsome:cons_app
gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0 :: Nat -> and:true:false:or:forall:nil:cons:forsome: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(and, true), true) -> true
app(app(and, x), false) -> false
app(app(and, false), y) -> false
app(app(or, true), y) -> true
app(app(or, x), true) -> true
app(app(or, false), false) -> false
app(app(forall, p), nil) -> true
app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
app(app(forsome, p), nil) -> false
app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))
encArg(and) -> and
encArg(true) -> true
encArg(false) -> false
encArg(or) -> or
encArg(forall) -> forall
encArg(nil) -> nil
encArg(cons) -> cons
encArg(forsome) -> forsome
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_and -> and
encode_true -> true
encode_false -> false
encode_or -> or
encode_forall -> forall
encode_nil -> nil
encode_cons -> cons
encode_forsome -> forsome

Types:
app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
and :: and:true:false:or:forall:nil:cons:forsome:cons_app
true :: and:true:false:or:forall:nil:cons:forsome:cons_app
false :: and:true:false:or:forall:nil:cons:forsome:cons_app
or :: and:true:false:or:forall:nil:cons:forsome:cons_app
forall :: and:true:false:or:forall:nil:cons:forsome:cons_app
nil :: and:true:false:or:forall:nil:cons:forsome:cons_app
cons :: and:true:false:or:forall:nil:cons:forsome:cons_app
forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app
encArg :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
cons_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
encode_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app
encode_and :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_true :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_false :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_or :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_forall :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_nil :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_cons :: and:true:false:or:forall:nil:cons:forsome:cons_app
encode_forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app
hole_and:true:false:or:forall:nil:cons:forsome:cons_app1_0 :: and:true:false:or:forall:nil:cons:forsome:cons_app
gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0 :: Nat -> and:true:false:or:forall:nil:cons:forsome:cons_app


Generator Equations:
gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(0) <=> and
gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(+(x, 1)) <=> cons_app(and, gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(x))


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

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

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(n4548_0)) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(0))

Induction Step:
encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(+(n4548_0, 1))) ->_R^Omega(0)
app(encArg(and), encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(n4548_0))) ->_R^Omega(0)
app(and, encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(n4548_0))) ->_IH
app(and, *3_0)

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

(12)
BOUNDS(1, INF)

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

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

(14)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   app(app(and, true), true) -> true
   app(app(and, x), false) -> false
   app(app(and, false), y) -> false
   app(app(or, true), y) -> true
   app(app(or, x), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, p), nil) -> true
   app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(app(forsome, p), nil) -> false
   app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))

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

   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome

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(and, true), true) -> true
   app(app(and, x), false) -> false
   app(app(and, false), y) -> false
   app(app(or, true), y) -> true
   app(app(or, x), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, p), nil) -> true
   app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(app(forsome, p), nil) -> false
   app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome

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

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

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


The TRS R consists of the following rules:

   app(c_app(forsome, p), nil) -> false
   app(c_app(and, true), true) -> true
   app(c_app(and, x), false) -> false
   app(c_app(or, x), true) -> true
   app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs))
   app(c_app(and, false), y) -> false
   app(c_app(forall, p), nil) -> true
   app(c_app(or, false), false) -> false
   app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs))
   app(c_app(or, true), y) -> true

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

   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   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_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome
   app(x0, x1) -> c_app(x0, x1)

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

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

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


The TRS R consists of the following rules:

   app(c_app(forsome, p), nil) -> false [1]
   app(c_app(and, true), true) -> true [1]
   app(c_app(and, x), false) -> false [1]
   app(c_app(or, x), true) -> true [1]
   app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1]
   app(c_app(and, false), y) -> false [1]
   app(c_app(forall, p), nil) -> true [1]
   app(c_app(or, false), false) -> false [1]
   app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1]
   app(c_app(or, true), y) -> true [1]
   encArg(and) -> and [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(forall) -> forall [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(forsome) -> forsome [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_and -> and [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_forall -> forall [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_forsome -> forsome [0]
   app(x0, x1) -> c_app(x0, x1) [0]

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

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

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

   app(c_app(forsome, p), nil) -> false [1]
   app(c_app(and, true), true) -> true [1]
   app(c_app(and, x), false) -> false [1]
   app(c_app(or, x), true) -> true [1]
   app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1]
   app(c_app(and, false), y) -> false [1]
   app(c_app(forall, p), nil) -> true [1]
   app(c_app(or, false), false) -> false [1]
   app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1]
   app(c_app(or, true), y) -> true [1]
   encArg(and) -> and [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(forall) -> forall [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(forsome) -> forsome [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_and -> and [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_forall -> forall [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_forsome -> forsome [0]
   app(x0, x1) -> c_app(x0, x1) [0]

The TRS has the following type information:
app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
c_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
cons_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app
encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons: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_and
   encode_true
   encode_false
   encode_or
   encode_forall
   encode_nil
   encode_cons
   encode_forsome
   app_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_and -> null_encode_and [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_forall -> null_encode_forall [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_forsome -> null_encode_forsome [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_and, null_encode_true, null_encode_false, null_encode_or, null_encode_forall, null_encode_nil, null_encode_cons, null_encode_forsome, null_app

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

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

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

   app(c_app(forsome, p), nil) -> false [1]
   app(c_app(and, true), true) -> true [1]
   app(c_app(and, x), false) -> false [1]
   app(c_app(or, x), true) -> true [1]
   app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1]
   app(c_app(and, false), y) -> false [1]
   app(c_app(forall, p), nil) -> true [1]
   app(c_app(or, false), false) -> false [1]
   app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1]
   app(c_app(or, true), y) -> true [1]
   encArg(and) -> and [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(forall) -> forall [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(forsome) -> forsome [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_and -> and [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_forall -> forall [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_forsome -> forsome [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_and -> null_encode_and [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_forall -> null_encode_forall [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_forsome -> null_encode_forsome [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
c_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
cons_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app

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

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

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

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

   app(c_app(forsome, p), nil) -> false [1]
   app(c_app(and, true), true) -> true [1]
   app(c_app(and, x), false) -> false [1]
   app(c_app(or, x), true) -> true [1]
   app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1]
   app(c_app(and, false), y) -> false [1]
   app(c_app(forall, p), nil) -> true [1]
   app(c_app(or, false), false) -> false [1]
   app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1]
   app(c_app(or, true), y) -> true [1]
   encArg(and) -> and [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(forall) -> forall [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(forsome) -> forsome [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_and -> and [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_forall -> forall [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_forsome -> forsome [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_and -> null_encode_and [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_forall -> null_encode_forall [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_forsome -> null_encode_forsome [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
c_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
cons_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome: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:

   forsome => 4
   nil => 5
   false => 2
   and => 0
   true => 7
   or => 6
   forall => 3
   cons => 1
   null_encArg => 0
   null_encode_app => 0
   null_encode_and => 0
   null_encode_true => 0
   null_encode_false => 0
   null_encode_or => 0
   null_encode_forall => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_forsome => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> app(app(6, app(p, x)), app(app(4, p), xs)) :|: xs >= 0, x >= 0, p >= 0, z = 1 + 4 + p, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, app(p, x)), app(app(3, p), xs)) :|: xs >= 0, x >= 0, z = 1 + 3 + p, p >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 0 + 7, z' = 7
   app(z, z') -{ 1 }-> 7 :|: x >= 0, z' = 7, z = 1 + 6 + x
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 3 + p, p >= 0, z' = 5
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, y >= 0, z' = y
   app(z, z') -{ 1 }-> 2 :|: p >= 0, z = 1 + 4 + p, z' = 5
   app(z, z') -{ 1 }-> 2 :|: z' = 2, x >= 0, z = 1 + 0 + x
   app(z, z') -{ 1 }-> 2 :|: z = 1 + 0 + 2, y >= 0, z' = y
   app(z, z') -{ 1 }-> 2 :|: z = 1 + 6 + 2, z' = 2
   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 }-> 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_and -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_forall -{ 0 }-> 3 :|: 
   encode_forall -{ 0 }-> 0 :|: 
   encode_forsome -{ 0 }-> 4 :|: 
   encode_forsome -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 5 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_or -{ 0 }-> 6 :|: 
   encode_or -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 7 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

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

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

   app(z, z') -{ 1 }-> app(app(6, app(z - 5, x)), app(app(4, z - 5), xs)) :|: xs >= 0, x >= 0, z - 5 >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, app(z - 4, x)), app(app(3, z - 4), xs)) :|: xs >= 0, x >= 0, z - 4 >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 0 + 7, z' = 7
   app(z, z') -{ 1 }-> 7 :|: z - 7 >= 0, z' = 7
   app(z, z') -{ 1 }-> 7 :|: z - 4 >= 0, z' = 5
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' >= 0
   app(z, z') -{ 1 }-> 2 :|: z - 5 >= 0, z' = 5
   app(z, z') -{ 1 }-> 2 :|: z' = 2, z - 1 >= 0
   app(z, z') -{ 1 }-> 2 :|: z = 1 + 0 + 2, z' >= 0
   app(z, z') -{ 1 }-> 2 :|: z = 1 + 6 + 2, z' = 2
   app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   app(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 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_and -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_forall -{ 0 }-> 3 :|: 
   encode_forall -{ 0 }-> 0 :|: 
   encode_forsome -{ 0 }-> 4 :|: 
   encode_forsome -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 5 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_or -{ 0 }-> 6 :|: 
   encode_or -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 7 :|: 
   encode_true -{ 0 }-> 0 :|: 


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

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

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_and -> null_encode_and [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_forall -> null_encode_forall [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_forsome -> null_encode_forsome [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_and, null_encode_true, null_encode_false, null_encode_or, null_encode_forall, null_encode_nil, null_encode_cons, null_encode_forsome, null_app

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

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

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

   app(c_app(forsome, p), nil) -> false [1]
   app(c_app(and, true), true) -> true [1]
   app(c_app(and, x), false) -> false [1]
   app(c_app(or, x), true) -> true [1]
   app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1]
   app(c_app(and, false), y) -> false [1]
   app(c_app(forall, p), nil) -> true [1]
   app(c_app(or, false), false) -> false [1]
   app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1]
   app(c_app(or, true), y) -> true [1]
   encArg(and) -> and [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(forall) -> forall [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(forsome) -> forsome [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_and -> and [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_forall -> forall [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_forsome -> forsome [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_and -> null_encode_and [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_forall -> null_encode_forall [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_forsome -> null_encode_forsome [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
c_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
cons_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encArg :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_and :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_true :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_false :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_or :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_forall :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_nil :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_cons :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_encode_forsome :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app
null_app :: forsome:c_app:nil:false:and:true:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome: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:

   forsome => 4
   nil => 5
   false => 2
   and => 0
   true => 7
   or => 6
   forall => 3
   cons => 1
   null_encArg => 0
   null_encode_app => 0
   null_encode_and => 0
   null_encode_true => 0
   null_encode_false => 0
   null_encode_or => 0
   null_encode_forall => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_forsome => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> app(app(6, app(p, x)), app(app(4, p), xs)) :|: xs >= 0, x >= 0, p >= 0, z = 1 + 4 + p, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, app(p, x)), app(app(3, p), xs)) :|: xs >= 0, x >= 0, z = 1 + 3 + p, p >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 0 + 7, z' = 7
   app(z, z') -{ 1 }-> 7 :|: x >= 0, z' = 7, z = 1 + 6 + x
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 3 + p, p >= 0, z' = 5
   app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, y >= 0, z' = y
   app(z, z') -{ 1 }-> 2 :|: p >= 0, z = 1 + 4 + p, z' = 5
   app(z, z') -{ 1 }-> 2 :|: z' = 2, x >= 0, z = 1 + 0 + x
   app(z, z') -{ 1 }-> 2 :|: z = 1 + 0 + 2, y >= 0, z' = y
   app(z, z') -{ 1 }-> 2 :|: z = 1 + 6 + 2, z' = 2
   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 }-> 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_and -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_forall -{ 0 }-> 3 :|: 
   encode_forall -{ 0 }-> 0 :|: 
   encode_forsome -{ 0 }-> 4 :|: 
   encode_forsome -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 5 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_or -{ 0 }-> 6 :|: 
   encode_or -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 7 :|: 
   encode_true -{ 0 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.

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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   ENCARG(and) -> c
   ENCARG(true) -> c1
   ENCARG(false) -> c2
   ENCARG(or) -> c3
   ENCARG(forall) -> c4
   ENCARG(nil) -> c5
   ENCARG(cons) -> c6
   ENCARG(forsome) -> c7
   ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_AND -> c10
   ENCODE_TRUE -> c11
   ENCODE_FALSE -> c12
   ENCODE_OR -> c13
   ENCODE_FORALL -> c14
   ENCODE_NIL -> c15
   ENCODE_CONS -> c16
   ENCODE_FORSOME -> c17
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0))
   APP(app(forsome, z0), nil) -> c26
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0))
   APP(app(forsome, z0), nil) -> c26
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_AND, ENCODE_TRUE, ENCODE_FALSE, ENCODE_OR, ENCODE_FORALL, ENCODE_NIL, ENCODE_CONS, ENCODE_FORSOME, APP_2

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7, c8_3, c9_3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25_5, c26, c27_5


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

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 16 trailing nodes:
   ENCODE_FORALL -> c14
   ENCARG(forall) -> c4
   ENCODE_CONS -> c16
   ENCARG(and) -> c
   ENCARG(cons) -> c6
   ENCARG(or) -> c3
   ENCODE_FORSOME -> c17
   ENCODE_NIL -> c15
   ENCODE_AND -> c10
   ENCODE_TRUE -> c11
   ENCODE_FALSE -> c12
   ENCARG(forsome) -> c7
   ENCODE_OR -> c13
   ENCARG(nil) -> c5
   ENCARG(true) -> c1
   ENCARG(false) -> c2

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0))
   APP(app(forsome, z0), nil) -> c26
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0))
   APP(app(forsome, z0), nil) -> c26
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c8_3, c9_3, c18, c19, c20, c21, c22, c23, c24, c25_5, c26, c27_5


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

(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c8_3, c9_3, c18, c19, c20, c21, c22, c23, c24, c26, c25_3, c27_3


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCODE_APP(z0, z1) -> c(ENCARG(z0))
   ENCODE_APP(z0, z1) -> c(ENCARG(z1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c8_3, c18, c19, c20, c21, c22, c23, c24, c26, c25_3, c27_3, c_1


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

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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c8_3, c18, c19, c20, c21, c22, c23, c24, c26, c25_3, c27_3, c_1


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

(45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_and -> and
   encode_true -> true
   encode_false -> false
   encode_or -> or
   encode_forall -> forall
   encode_nil -> nil
   encode_cons -> cons
   encode_forsome -> forsome

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c8_3, c18, c19, c20, c21, c22, c23, c24, c26, c25_3, c27_3, c_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0), ENCARG(and))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0), ENCARG(or))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0), ENCARG(forall))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0), ENCARG(forsome))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(and, x1)) -> c8(APP(and, encArg(x1)), ENCARG(and), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(APP(or, encArg(x1)), ENCARG(or), ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(APP(forall, encArg(x1)), ENCARG(forall), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(APP(forsome, encArg(x1)), ENCARG(forsome), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0), ENCARG(and))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0), ENCARG(or))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0), ENCARG(forall))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0), ENCARG(forsome))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(and, x1)) -> c8(APP(and, encArg(x1)), ENCARG(and), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(APP(or, encArg(x1)), ENCARG(or), ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(APP(forall, encArg(x1)), ENCARG(forall), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(APP(forsome, encArg(x1)), ENCARG(forsome), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c25_3, c27_3, c_1, c8_3


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

(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 24 trailing tuple parts
----------------------------------------

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2))
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c25_3, c27_3, c_1, c8_3, c8_2, c8_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, z0), app(app(cons, z1), z2)) -> c25(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) by 
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c27_3, c_1, c8_3, c8_2, c8_1, c25_3


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, z0), app(app(cons, z1), z2)) -> c27(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) by 
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c_1, c8_3, c8_2, c8_1, c25_3, c27_3


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(and, x1) -> c(APP(and, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(or, x1) -> c(APP(or, encArg(x1)))
   ENCODE_APP(forall, x1) -> c(APP(forall, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(forsome, x1) -> c(APP(forsome, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(and, x1) -> c(APP(and, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(or, x1) -> c(APP(or, encArg(x1)))
   ENCODE_APP(forall, x1) -> c(APP(forall, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(forsome, x1) -> c(APP(forsome, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_3, c8_2, c8_1, c25_3, c27_3, c_1


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(or, x1) -> c(APP(or, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(forsome, x1) -> c(APP(forsome, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(forall, x1) -> c(APP(forall, encArg(x1)))
   ENCODE_APP(and, x1) -> c(APP(and, encArg(x1)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_3, c8_2, c8_1, c25_3, c27_3, c_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(APP(and, app(encArg(x1), encArg(x2))), ENCARG(and), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(APP(or, app(encArg(x1), encArg(x2))), ENCARG(or), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(APP(forall, app(encArg(x1), encArg(x2))), ENCARG(forall), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(APP(forsome, app(encArg(x1), encArg(x2))), ENCARG(forsome), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(APP(and, app(encArg(x1), encArg(x2))), ENCARG(and), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(APP(or, app(encArg(x1), encArg(x2))), ENCARG(or), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(APP(forall, app(encArg(x1), encArg(x2))), ENCARG(forall), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(APP(forsome, app(encArg(x1), encArg(x2))), ENCARG(forsome), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(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(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_3, c8_2, c8_1, c25_3, c27_3, c_1


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_3, c8_2, c8_1, c25_3, c27_3, c_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)), ENCARG(and))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)), ENCARG(or))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)), ENCARG(forall))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)), ENCARG(forsome))
   ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c8(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, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)), ENCARG(and))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)), ENCARG(or))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)), ENCARG(forall))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)), ENCARG(forsome))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0)) by 
   ENCARG(cons_app(and, and)) -> c8(APP(and, and), ENCARG(and))
   ENCARG(cons_app(true, and)) -> c8(APP(true, and), ENCARG(true))
   ENCARG(cons_app(false, and)) -> c8(APP(false, and), ENCARG(false))
   ENCARG(cons_app(or, and)) -> c8(APP(or, and), ENCARG(or))
   ENCARG(cons_app(forall, and)) -> c8(APP(forall, and), ENCARG(forall))
   ENCARG(cons_app(nil, and)) -> c8(APP(nil, and), ENCARG(nil))
   ENCARG(cons_app(cons, and)) -> c8(APP(cons, and), ENCARG(cons))
   ENCARG(cons_app(forsome, and)) -> c8(APP(forsome, and), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), and)) -> c8(APP(app(encArg(z0), encArg(z1)), and), ENCARG(cons_app(z0, z1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, and)) -> c8(APP(and, and), ENCARG(and))
   ENCARG(cons_app(true, and)) -> c8(APP(true, and), ENCARG(true))
   ENCARG(cons_app(false, and)) -> c8(APP(false, and), ENCARG(false))
   ENCARG(cons_app(or, and)) -> c8(APP(or, and), ENCARG(or))
   ENCARG(cons_app(forall, and)) -> c8(APP(forall, and), ENCARG(forall))
   ENCARG(cons_app(nil, and)) -> c8(APP(nil, and), ENCARG(nil))
   ENCARG(cons_app(cons, and)) -> c8(APP(cons, and), ENCARG(cons))
   ENCARG(cons_app(forsome, and)) -> c8(APP(forsome, and), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(forsome, and)) -> c8(APP(forsome, and), ENCARG(forsome))
   ENCARG(cons_app(or, and)) -> c8(APP(or, and), ENCARG(or))
   ENCARG(cons_app(and, and)) -> c8(APP(and, and), ENCARG(and))
   ENCARG(cons_app(cons, and)) -> c8(APP(cons, and), ENCARG(cons))
   ENCARG(cons_app(true, and)) -> c8(APP(true, and), ENCARG(true))
   ENCARG(cons_app(nil, and)) -> c8(APP(nil, and), ENCARG(nil))
   ENCARG(cons_app(false, and)) -> c8(APP(false, and), ENCARG(false))
   ENCARG(cons_app(forall, and)) -> c8(APP(forall, and), ENCARG(forall))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) by 
   ENCARG(cons_app(and, true)) -> c8(APP(and, true), ENCARG(and))
   ENCARG(cons_app(true, true)) -> c8(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c8(APP(false, true), ENCARG(false))
   ENCARG(cons_app(or, true)) -> c8(APP(or, true), ENCARG(or))
   ENCARG(cons_app(forall, true)) -> c8(APP(forall, true), ENCARG(forall))
   ENCARG(cons_app(nil, true)) -> c8(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c8(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(forsome, true)) -> c8(APP(forsome, true), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), true)) -> c8(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, true)) -> c8(APP(and, true), ENCARG(and))
   ENCARG(cons_app(true, true)) -> c8(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c8(APP(false, true), ENCARG(false))
   ENCARG(cons_app(or, true)) -> c8(APP(or, true), ENCARG(or))
   ENCARG(cons_app(forall, true)) -> c8(APP(forall, true), ENCARG(forall))
   ENCARG(cons_app(nil, true)) -> c8(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c8(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(forsome, true)) -> c8(APP(forsome, true), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(and, true)) -> c8(APP(and, true), ENCARG(and))
   ENCARG(cons_app(cons, true)) -> c8(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(forall, true)) -> c8(APP(forall, true), ENCARG(forall))
   ENCARG(cons_app(nil, true)) -> c8(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(false, true)) -> c8(APP(false, true), ENCARG(false))
   ENCARG(cons_app(true, true)) -> c8(APP(true, true), ENCARG(true))
   ENCARG(cons_app(forsome, true)) -> c8(APP(forsome, true), ENCARG(forsome))
   ENCARG(cons_app(or, true)) -> c8(APP(or, true), ENCARG(or))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) by 
   ENCARG(cons_app(and, false)) -> c8(APP(and, false), ENCARG(and))
   ENCARG(cons_app(true, false)) -> c8(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c8(APP(false, false), ENCARG(false))
   ENCARG(cons_app(or, false)) -> c8(APP(or, false), ENCARG(or))
   ENCARG(cons_app(forall, false)) -> c8(APP(forall, false), ENCARG(forall))
   ENCARG(cons_app(nil, false)) -> c8(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c8(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(forsome, false)) -> c8(APP(forsome, false), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), false)) -> c8(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, false)) -> c8(APP(and, false), ENCARG(and))
   ENCARG(cons_app(true, false)) -> c8(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c8(APP(false, false), ENCARG(false))
   ENCARG(cons_app(or, false)) -> c8(APP(or, false), ENCARG(or))
   ENCARG(cons_app(forall, false)) -> c8(APP(forall, false), ENCARG(forall))
   ENCARG(cons_app(nil, false)) -> c8(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c8(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(forsome, false)) -> c8(APP(forsome, false), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(and, false)) -> c8(APP(and, false), ENCARG(and))
   ENCARG(cons_app(true, false)) -> c8(APP(true, false), ENCARG(true))
   ENCARG(cons_app(forsome, false)) -> c8(APP(forsome, false), ENCARG(forsome))
   ENCARG(cons_app(or, false)) -> c8(APP(or, false), ENCARG(or))
   ENCARG(cons_app(nil, false)) -> c8(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c8(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(false, false)) -> c8(APP(false, false), ENCARG(false))
   ENCARG(cons_app(forall, false)) -> c8(APP(forall, false), ENCARG(forall))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0)) by 
   ENCARG(cons_app(and, or)) -> c8(APP(and, or), ENCARG(and))
   ENCARG(cons_app(true, or)) -> c8(APP(true, or), ENCARG(true))
   ENCARG(cons_app(false, or)) -> c8(APP(false, or), ENCARG(false))
   ENCARG(cons_app(or, or)) -> c8(APP(or, or), ENCARG(or))
   ENCARG(cons_app(forall, or)) -> c8(APP(forall, or), ENCARG(forall))
   ENCARG(cons_app(nil, or)) -> c8(APP(nil, or), ENCARG(nil))
   ENCARG(cons_app(cons, or)) -> c8(APP(cons, or), ENCARG(cons))
   ENCARG(cons_app(forsome, or)) -> c8(APP(forsome, or), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), or)) -> c8(APP(app(encArg(z0), encArg(z1)), or), ENCARG(cons_app(z0, z1)))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, or)) -> c8(APP(and, or), ENCARG(and))
   ENCARG(cons_app(true, or)) -> c8(APP(true, or), ENCARG(true))
   ENCARG(cons_app(false, or)) -> c8(APP(false, or), ENCARG(false))
   ENCARG(cons_app(or, or)) -> c8(APP(or, or), ENCARG(or))
   ENCARG(cons_app(forall, or)) -> c8(APP(forall, or), ENCARG(forall))
   ENCARG(cons_app(nil, or)) -> c8(APP(nil, or), ENCARG(nil))
   ENCARG(cons_app(cons, or)) -> c8(APP(cons, or), ENCARG(cons))
   ENCARG(cons_app(forsome, or)) -> c8(APP(forsome, or), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(forsome, or)) -> c8(APP(forsome, or), ENCARG(forsome))
   ENCARG(cons_app(or, or)) -> c8(APP(or, or), ENCARG(or))
   ENCARG(cons_app(forall, or)) -> c8(APP(forall, or), ENCARG(forall))
   ENCARG(cons_app(true, or)) -> c8(APP(true, or), ENCARG(true))
   ENCARG(cons_app(false, or)) -> c8(APP(false, or), ENCARG(false))
   ENCARG(cons_app(cons, or)) -> c8(APP(cons, or), ENCARG(cons))
   ENCARG(cons_app(nil, or)) -> c8(APP(nil, or), ENCARG(nil))
   ENCARG(cons_app(and, or)) -> c8(APP(and, or), ENCARG(and))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0)) by 
   ENCARG(cons_app(and, forall)) -> c8(APP(and, forall), ENCARG(and))
   ENCARG(cons_app(true, forall)) -> c8(APP(true, forall), ENCARG(true))
   ENCARG(cons_app(false, forall)) -> c8(APP(false, forall), ENCARG(false))
   ENCARG(cons_app(or, forall)) -> c8(APP(or, forall), ENCARG(or))
   ENCARG(cons_app(forall, forall)) -> c8(APP(forall, forall), ENCARG(forall))
   ENCARG(cons_app(nil, forall)) -> c8(APP(nil, forall), ENCARG(nil))
   ENCARG(cons_app(cons, forall)) -> c8(APP(cons, forall), ENCARG(cons))
   ENCARG(cons_app(forsome, forall)) -> c8(APP(forsome, forall), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), forall)) -> c8(APP(app(encArg(z0), encArg(z1)), forall), ENCARG(cons_app(z0, z1)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, forall)) -> c8(APP(and, forall), ENCARG(and))
   ENCARG(cons_app(true, forall)) -> c8(APP(true, forall), ENCARG(true))
   ENCARG(cons_app(false, forall)) -> c8(APP(false, forall), ENCARG(false))
   ENCARG(cons_app(or, forall)) -> c8(APP(or, forall), ENCARG(or))
   ENCARG(cons_app(forall, forall)) -> c8(APP(forall, forall), ENCARG(forall))
   ENCARG(cons_app(nil, forall)) -> c8(APP(nil, forall), ENCARG(nil))
   ENCARG(cons_app(cons, forall)) -> c8(APP(cons, forall), ENCARG(cons))
   ENCARG(cons_app(forsome, forall)) -> c8(APP(forsome, forall), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(false, forall)) -> c8(APP(false, forall), ENCARG(false))
   ENCARG(cons_app(true, forall)) -> c8(APP(true, forall), ENCARG(true))
   ENCARG(cons_app(forall, forall)) -> c8(APP(forall, forall), ENCARG(forall))
   ENCARG(cons_app(forsome, forall)) -> c8(APP(forsome, forall), ENCARG(forsome))
   ENCARG(cons_app(or, forall)) -> c8(APP(or, forall), ENCARG(or))
   ENCARG(cons_app(and, forall)) -> c8(APP(and, forall), ENCARG(and))
   ENCARG(cons_app(cons, forall)) -> c8(APP(cons, forall), ENCARG(cons))
   ENCARG(cons_app(nil, forall)) -> c8(APP(nil, forall), ENCARG(nil))

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(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(and, nil)) -> c8(APP(and, nil), ENCARG(and))
   ENCARG(cons_app(true, nil)) -> c8(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c8(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(or, nil)) -> c8(APP(or, nil), ENCARG(or))
   ENCARG(cons_app(forall, nil)) -> c8(APP(forall, nil), ENCARG(forall))
   ENCARG(cons_app(nil, nil)) -> c8(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c8(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(forsome, nil)) -> c8(APP(forsome, nil), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c8(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, nil)) -> c8(APP(and, nil), ENCARG(and))
   ENCARG(cons_app(true, nil)) -> c8(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c8(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(or, nil)) -> c8(APP(or, nil), ENCARG(or))
   ENCARG(cons_app(forall, nil)) -> c8(APP(forall, nil), ENCARG(forall))
   ENCARG(cons_app(nil, nil)) -> c8(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c8(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(forsome, nil)) -> c8(APP(forsome, nil), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(forsome, nil)) -> c8(APP(forsome, nil), ENCARG(forsome))
   ENCARG(cons_app(nil, nil)) -> c8(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(or, nil)) -> c8(APP(or, nil), ENCARG(or))
   ENCARG(cons_app(true, nil)) -> c8(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(forall, nil)) -> c8(APP(forall, nil), ENCARG(forall))
   ENCARG(cons_app(and, nil)) -> c8(APP(and, nil), ENCARG(and))
   ENCARG(cons_app(cons, nil)) -> c8(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(false, nil)) -> c8(APP(false, nil), ENCARG(false))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(and, cons)) -> c8(APP(and, cons), ENCARG(and))
   ENCARG(cons_app(true, cons)) -> c8(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c8(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(or, cons)) -> c8(APP(or, cons), ENCARG(or))
   ENCARG(cons_app(forall, cons)) -> c8(APP(forall, cons), ENCARG(forall))
   ENCARG(cons_app(nil, cons)) -> c8(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c8(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(forsome, cons)) -> c8(APP(forsome, cons), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c8(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, cons)) -> c8(APP(and, cons), ENCARG(and))
   ENCARG(cons_app(true, cons)) -> c8(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c8(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(or, cons)) -> c8(APP(or, cons), ENCARG(or))
   ENCARG(cons_app(forall, cons)) -> c8(APP(forall, cons), ENCARG(forall))
   ENCARG(cons_app(nil, cons)) -> c8(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c8(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(forsome, cons)) -> c8(APP(forsome, cons), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(true, cons)) -> c8(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c8(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(nil, cons)) -> c8(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(forsome, cons)) -> c8(APP(forsome, cons), ENCARG(forsome))
   ENCARG(cons_app(or, cons)) -> c8(APP(or, cons), ENCARG(or))
   ENCARG(cons_app(forall, cons)) -> c8(APP(forall, cons), ENCARG(forall))
   ENCARG(cons_app(and, cons)) -> c8(APP(and, cons), ENCARG(and))
   ENCARG(cons_app(cons, cons)) -> c8(APP(cons, cons), ENCARG(cons))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0))
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_2, c8_1, c25_3, c27_3, c_1, c8_3


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0)) by 
   ENCARG(cons_app(and, forsome)) -> c8(APP(and, forsome), ENCARG(and))
   ENCARG(cons_app(true, forsome)) -> c8(APP(true, forsome), ENCARG(true))
   ENCARG(cons_app(false, forsome)) -> c8(APP(false, forsome), ENCARG(false))
   ENCARG(cons_app(or, forsome)) -> c8(APP(or, forsome), ENCARG(or))
   ENCARG(cons_app(forall, forsome)) -> c8(APP(forall, forsome), ENCARG(forall))
   ENCARG(cons_app(nil, forsome)) -> c8(APP(nil, forsome), ENCARG(nil))
   ENCARG(cons_app(cons, forsome)) -> c8(APP(cons, forsome), ENCARG(cons))
   ENCARG(cons_app(forsome, forsome)) -> c8(APP(forsome, forsome), ENCARG(forsome))
   ENCARG(cons_app(cons_app(z0, z1), forsome)) -> c8(APP(app(encArg(z0), encArg(z1)), forsome), ENCARG(cons_app(z0, z1)))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(and, forsome)) -> c8(APP(and, forsome), ENCARG(and))
   ENCARG(cons_app(true, forsome)) -> c8(APP(true, forsome), ENCARG(true))
   ENCARG(cons_app(false, forsome)) -> c8(APP(false, forsome), ENCARG(false))
   ENCARG(cons_app(or, forsome)) -> c8(APP(or, forsome), ENCARG(or))
   ENCARG(cons_app(forall, forsome)) -> c8(APP(forall, forsome), ENCARG(forall))
   ENCARG(cons_app(nil, forsome)) -> c8(APP(nil, forsome), ENCARG(nil))
   ENCARG(cons_app(cons, forsome)) -> c8(APP(cons, forsome), ENCARG(cons))
   ENCARG(cons_app(forsome, forsome)) -> c8(APP(forsome, forsome), ENCARG(forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2


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

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCARG(cons_app(and, forsome)) -> c8(APP(and, forsome), ENCARG(and))
   ENCARG(cons_app(nil, forsome)) -> c8(APP(nil, forsome), ENCARG(nil))
   ENCARG(cons_app(forsome, forsome)) -> c8(APP(forsome, forsome), ENCARG(forsome))
   ENCARG(cons_app(or, forsome)) -> c8(APP(or, forsome), ENCARG(or))
   ENCARG(cons_app(cons, forsome)) -> c8(APP(cons, forsome), ENCARG(cons))
   ENCARG(cons_app(false, forsome)) -> c8(APP(false, forsome), ENCARG(false))
   ENCARG(cons_app(forall, forsome)) -> c8(APP(forall, forsome), ENCARG(forall))
   ENCARG(cons_app(true, forsome)) -> c8(APP(true, forsome), ENCARG(true))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, z0), app(app(cons, x1), nil)) -> c25(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) by 
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c25(APP(app(and, false), true), APP(app(and, z0), false), APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c25(APP(app(and, false), true), APP(app(and, false), z0), APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c25(APP(app(and, true), true), APP(app(or, true), z0), APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(or, z0), true), APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c25(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c25(APP(app(and, true), true), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c25(APP(app(and, false), true), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c25(APP(app(and, false), true), APP(app(and, z0), false), APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c25(APP(app(and, false), true), APP(app(and, false), z0), APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c25(APP(app(and, true), true), APP(app(or, true), z0), APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(or, z0), true), APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c25(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c25(APP(app(and, true), true), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c25(APP(app(and, false), true), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c25(APP(app(and, false), true), APP(app(and, z0), false), APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c25(APP(app(and, false), true), APP(app(and, false), z0), APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c25(APP(app(and, true), true), APP(app(or, true), z0), APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(or, z0), true), APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c25(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c25(APP(app(and, true), true), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c25(APP(app(and, false), true), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1


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(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) by 
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))

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(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) by 
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, z1), z2))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), z1)), app(app(forall, app(and, true)), z2))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, z1), z2)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2


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

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, app(or, true)), app(app(cons, z0), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forall, app(or, true)), x2)) by 
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c25(APP(app(and, true), true), APP(app(or, true), x0), APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), app(app(cons, z1), z2))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), z1)), app(app(forall, app(or, true)), z2))), APP(app(or, true), x0), APP(app(forall, app(or, true)), app(app(cons, z1), z2)))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c25(APP(app(and, true), true), APP(app(or, true), x0), APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c25(APP(app(and, true), true), APP(app(or, true), x0), APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1


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

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, app(or, z0)), app(app(cons, true), x2)) -> c25(APP(app(and, true), app(app(forall, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forall, app(or, z0)), x2)) by 
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(or, x0), true), APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), app(app(cons, z1), z2))) -> c25(APP(app(and, true), app(app(and, app(app(or, x0), z1)), app(app(forall, app(or, x0)), z2))), APP(app(or, x0), true), APP(app(forall, app(or, x0)), app(app(cons, z1), z2)))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(or, x0), true), APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c25(APP(app(and, true), true), APP(app(or, x0), true), APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1


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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) by 
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c25(APP(app(and, true), true), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), app(app(cons, z1), z2))) -> c25(APP(app(and, true), app(app(and, app(app(forall, x0), z1)), app(app(forall, app(forall, x0)), z2))), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), app(app(cons, z1), z2)))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c25(APP(app(and, true), true), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c25(APP(app(and, true), true), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1


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

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) by 
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c25(APP(app(and, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), true), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c25(APP(app(and, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), app(app(and, app(app(forall, x0), z1)), app(app(forall, app(forall, x0)), z2))), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forall, app(forall, x0)), app(app(cons, z1), z2)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) by 
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c25(APP(app(and, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), true), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forall, app(forsome, x0)), nil))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c25(APP(app(and, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), app(app(and, app(app(forsome, x0), z1)), app(app(forall, app(forsome, x0)), z2))), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forall, app(forsome, x0)), app(app(cons, z1), z2)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, z0), app(app(cons, x1), nil)) -> c27(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) by 
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c27(APP(app(or, false), false), APP(app(and, false), z0), APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c27(APP(app(or, true), false), APP(app(or, true), z0), APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c27(APP(app(or, true), false), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c27(APP(app(or, true), false), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c27(APP(app(or, false), false), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c27(APP(app(or, false), false), APP(app(and, false), z0), APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c27(APP(app(or, true), false), APP(app(or, true), z0), APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c27(APP(app(or, true), false), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c27(APP(app(or, true), false), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c27(APP(app(or, false), false), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c27(APP(app(or, false), false), APP(app(and, false), z0), APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c27(APP(app(or, true), false), APP(app(or, true), z0), APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c27(APP(app(or, true), false), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c27(APP(app(or, true), false), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c27(APP(app(or, false), false), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1


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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) by 
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, app(and, z0)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), x2)) by 
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(and, x0), false), APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, x0)), app(app(cons, false), app(app(cons, z1), z2))) -> c27(APP(app(or, false), app(app(or, app(app(and, x0), z1)), app(app(forsome, app(and, x0)), z2))), APP(app(and, x0), false), APP(app(forsome, app(and, x0)), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(and, x0), false), APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(and, x0), false), APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2


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

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, app(and, false)), app(app(cons, z0), x2)) -> c27(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forsome, app(and, false)), x2)) by 
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c27(APP(app(or, false), false), APP(app(and, false), x0), APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), app(app(cons, z1), z2))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), z1)), app(app(forsome, app(and, false)), z2))), APP(app(and, false), x0), APP(app(forsome, app(and, false)), app(app(cons, z1), z2)))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c27(APP(app(or, false), false), APP(app(and, false), x0), APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c27(APP(app(or, false), false), APP(app(and, false), x0), APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) by 
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, z1), z2))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), z1)), app(app(forsome, app(or, false)), z2))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, z1), z2)))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) by 
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c27(APP(app(or, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), false), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forall, x0)), nil))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c27(APP(app(or, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), app(app(or, app(app(forall, x0), z1)), app(app(forsome, app(forall, x0)), z2))), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forall, x0)), app(app(cons, z1), z2)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) by 
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c27(APP(app(or, false), false), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), app(app(cons, z1), z2))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, x0), z1)), app(app(forsome, app(forsome, x0)), z2))), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), app(app(cons, z1), z2)))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c27(APP(app(or, false), false), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c27(APP(app(or, false), false), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) by 
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c27(APP(app(or, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), false), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c27(APP(app(or, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), app(app(or, app(app(forsome, x0), z1)), app(app(forsome, app(forsome, x0)), z2))), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forsome, x0)), app(app(cons, z1), z2)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, and) -> c(APP(encArg(x0), and))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, and) -> c(APP(encArg(x0), and)) by 
   ENCODE_APP(and, and) -> c(APP(and, and))
   ENCODE_APP(true, and) -> c(APP(true, and))
   ENCODE_APP(false, and) -> c(APP(false, and))
   ENCODE_APP(or, and) -> c(APP(or, and))
   ENCODE_APP(forall, and) -> c(APP(forall, and))
   ENCODE_APP(nil, and) -> c(APP(nil, and))
   ENCODE_APP(cons, and) -> c(APP(cons, and))
   ENCODE_APP(forsome, and) -> c(APP(forsome, and))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(and, and) -> c(APP(and, and))
   ENCODE_APP(true, and) -> c(APP(true, and))
   ENCODE_APP(false, and) -> c(APP(false, and))
   ENCODE_APP(or, and) -> c(APP(or, and))
   ENCODE_APP(forall, and) -> c(APP(forall, and))
   ENCODE_APP(nil, and) -> c(APP(nil, and))
   ENCODE_APP(cons, and) -> c(APP(cons, and))
   ENCODE_APP(forsome, and) -> c(APP(forsome, and))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(forsome, and) -> c(APP(forsome, and))
   ENCODE_APP(or, and) -> c(APP(or, and))
   ENCODE_APP(and, and) -> c(APP(and, and))
   ENCODE_APP(nil, and) -> c(APP(nil, and))
   ENCODE_APP(cons, and) -> c(APP(cons, and))
   ENCODE_APP(forall, and) -> c(APP(forall, and))
   ENCODE_APP(true, and) -> c(APP(true, and))
   ENCODE_APP(false, and) -> c(APP(false, and))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(155) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) by 
   ENCODE_APP(and, true) -> c(APP(and, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(or, true) -> c(APP(or, true))
   ENCODE_APP(forall, true) -> c(APP(forall, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(forsome, true) -> c(APP(forsome, true))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(and, true) -> c(APP(and, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(or, true) -> c(APP(or, true))
   ENCODE_APP(forall, true) -> c(APP(forall, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(forsome, true) -> c(APP(forsome, true))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(forall, true) -> c(APP(forall, true))
   ENCODE_APP(false, true) -> c(APP(false, true))
   ENCODE_APP(nil, true) -> c(APP(nil, true))
   ENCODE_APP(cons, true) -> c(APP(cons, true))
   ENCODE_APP(true, true) -> c(APP(true, true))
   ENCODE_APP(and, true) -> c(APP(and, true))
   ENCODE_APP(forsome, true) -> c(APP(forsome, true))
   ENCODE_APP(or, true) -> c(APP(or, true))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) by 
   ENCODE_APP(and, false) -> c(APP(and, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(or, false) -> c(APP(or, false))
   ENCODE_APP(forall, false) -> c(APP(forall, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(forsome, false) -> c(APP(forsome, false))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(and, false) -> c(APP(and, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(or, false) -> c(APP(or, false))
   ENCODE_APP(forall, false) -> c(APP(forall, false))
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(forsome, false) -> c(APP(forsome, false))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(nil, false) -> c(APP(nil, false))
   ENCODE_APP(and, false) -> c(APP(and, false))
   ENCODE_APP(false, false) -> c(APP(false, false))
   ENCODE_APP(cons, false) -> c(APP(cons, false))
   ENCODE_APP(true, false) -> c(APP(true, false))
   ENCODE_APP(forsome, false) -> c(APP(forsome, false))
   ENCODE_APP(or, false) -> c(APP(or, false))
   ENCODE_APP(forall, false) -> c(APP(forall, false))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(163) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, or) -> c(APP(encArg(x0), or)) by 
   ENCODE_APP(and, or) -> c(APP(and, or))
   ENCODE_APP(true, or) -> c(APP(true, or))
   ENCODE_APP(false, or) -> c(APP(false, or))
   ENCODE_APP(or, or) -> c(APP(or, or))
   ENCODE_APP(forall, or) -> c(APP(forall, or))
   ENCODE_APP(nil, or) -> c(APP(nil, or))
   ENCODE_APP(cons, or) -> c(APP(cons, or))
   ENCODE_APP(forsome, or) -> c(APP(forsome, or))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(and, or) -> c(APP(and, or))
   ENCODE_APP(true, or) -> c(APP(true, or))
   ENCODE_APP(false, or) -> c(APP(false, or))
   ENCODE_APP(or, or) -> c(APP(or, or))
   ENCODE_APP(forall, or) -> c(APP(forall, or))
   ENCODE_APP(nil, or) -> c(APP(nil, or))
   ENCODE_APP(cons, or) -> c(APP(cons, or))
   ENCODE_APP(forsome, or) -> c(APP(forsome, or))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(false, or) -> c(APP(false, or))
   ENCODE_APP(forsome, or) -> c(APP(forsome, or))
   ENCODE_APP(cons, or) -> c(APP(cons, or))
   ENCODE_APP(or, or) -> c(APP(or, or))
   ENCODE_APP(true, or) -> c(APP(true, or))
   ENCODE_APP(and, or) -> c(APP(and, or))
   ENCODE_APP(nil, or) -> c(APP(nil, or))
   ENCODE_APP(forall, or) -> c(APP(forall, or))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(167) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall)) by 
   ENCODE_APP(and, forall) -> c(APP(and, forall))
   ENCODE_APP(true, forall) -> c(APP(true, forall))
   ENCODE_APP(false, forall) -> c(APP(false, forall))
   ENCODE_APP(or, forall) -> c(APP(or, forall))
   ENCODE_APP(forall, forall) -> c(APP(forall, forall))
   ENCODE_APP(nil, forall) -> c(APP(nil, forall))
   ENCODE_APP(cons, forall) -> c(APP(cons, forall))
   ENCODE_APP(forsome, forall) -> c(APP(forsome, forall))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(and, forall) -> c(APP(and, forall))
   ENCODE_APP(true, forall) -> c(APP(true, forall))
   ENCODE_APP(false, forall) -> c(APP(false, forall))
   ENCODE_APP(or, forall) -> c(APP(or, forall))
   ENCODE_APP(forall, forall) -> c(APP(forall, forall))
   ENCODE_APP(nil, forall) -> c(APP(nil, forall))
   ENCODE_APP(cons, forall) -> c(APP(cons, forall))
   ENCODE_APP(forsome, forall) -> c(APP(forsome, forall))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(forall, forall) -> c(APP(forall, forall))
   ENCODE_APP(false, forall) -> c(APP(false, forall))
   ENCODE_APP(cons, forall) -> c(APP(cons, forall))
   ENCODE_APP(nil, forall) -> c(APP(nil, forall))
   ENCODE_APP(true, forall) -> c(APP(true, forall))
   ENCODE_APP(and, forall) -> c(APP(and, forall))
   ENCODE_APP(forsome, forall) -> c(APP(forsome, forall))
   ENCODE_APP(or, forall) -> c(APP(or, forall))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(171) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by 
   ENCODE_APP(and, nil) -> c(APP(and, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(or, nil) -> c(APP(or, nil))
   ENCODE_APP(forall, nil) -> c(APP(forall, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(forsome, nil) -> c(APP(forsome, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   ENCODE_APP(and, nil) -> c(APP(and, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(or, nil) -> c(APP(or, nil))
   ENCODE_APP(forall, nil) -> c(APP(forall, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(forsome, nil) -> c(APP(forsome, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(forall, nil) -> c(APP(forall, nil))
   ENCODE_APP(forsome, nil) -> c(APP(forsome, nil))
   ENCODE_APP(or, nil) -> c(APP(or, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(and, nil) -> c(APP(and, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) by 
   ENCODE_APP(and, cons) -> c(APP(and, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(or, cons) -> c(APP(or, cons))
   ENCODE_APP(forall, cons) -> c(APP(forall, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(forsome, cons) -> c(APP(forsome, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(and, cons) -> c(APP(and, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(or, cons) -> c(APP(or, cons))
   ENCODE_APP(forall, cons) -> c(APP(forall, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(forsome, cons) -> c(APP(forsome, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(forsome, cons) -> c(APP(forsome, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(or, cons) -> c(APP(or, cons))
   ENCODE_APP(and, cons) -> c(APP(and, cons))
   ENCODE_APP(forall, cons) -> c(APP(forall, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   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(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(179) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome)) by 
   ENCODE_APP(and, forsome) -> c(APP(and, forsome))
   ENCODE_APP(true, forsome) -> c(APP(true, forsome))
   ENCODE_APP(false, forsome) -> c(APP(false, forsome))
   ENCODE_APP(or, forsome) -> c(APP(or, forsome))
   ENCODE_APP(forall, forsome) -> c(APP(forall, forsome))
   ENCODE_APP(nil, forsome) -> c(APP(nil, forsome))
   ENCODE_APP(cons, forsome) -> c(APP(cons, forsome))
   ENCODE_APP(forsome, forsome) -> c(APP(forsome, forsome))
   ENCODE_APP(cons_app(z0, z1), forsome) -> c(APP(app(encArg(z0), encArg(z1)), forsome))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   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(and, forsome) -> c(APP(and, forsome))
   ENCODE_APP(true, forsome) -> c(APP(true, forsome))
   ENCODE_APP(false, forsome) -> c(APP(false, forsome))
   ENCODE_APP(or, forsome) -> c(APP(or, forsome))
   ENCODE_APP(forall, forsome) -> c(APP(forall, forsome))
   ENCODE_APP(nil, forsome) -> c(APP(nil, forsome))
   ENCODE_APP(cons, forsome) -> c(APP(cons, forsome))
   ENCODE_APP(forsome, forsome) -> c(APP(forsome, forsome))
   ENCODE_APP(cons_app(z0, z1), forsome) -> c(APP(app(encArg(z0), encArg(z1)), forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(and, forsome) -> c(APP(and, forsome))
   ENCODE_APP(cons, forsome) -> c(APP(cons, forsome))
   ENCODE_APP(forall, forsome) -> c(APP(forall, forsome))
   ENCODE_APP(nil, forsome) -> c(APP(nil, forsome))
   ENCODE_APP(false, forsome) -> c(APP(false, forsome))
   ENCODE_APP(forsome, forsome) -> c(APP(forsome, forsome))
   ENCODE_APP(or, forsome) -> c(APP(or, forsome))
   ENCODE_APP(true, forsome) -> c(APP(true, forsome))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   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), forsome) -> c(APP(app(encArg(z0), encArg(z1)), forsome))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(183) 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, and)) -> c(APP(encArg(x0), app(encArg(x1), and)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, or)) -> c(APP(encArg(x0), app(encArg(x1), or)))
   ENCODE_APP(x0, cons_app(x1, forall)) -> c(APP(encArg(x0), app(encArg(x1), forall)))
   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, forsome)) -> c(APP(encArg(x0), app(encArg(x1), forsome)))
   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(and, x2)) -> c(APP(encArg(x0), app(and, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(or, x2)) -> c(APP(encArg(x0), app(or, encArg(x2))))
   ENCODE_APP(x0, cons_app(forall, x2)) -> c(APP(encArg(x0), app(forall, 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(forsome, x2)) -> c(APP(encArg(x0), app(forsome, 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(and, cons_app(x1, x2)) -> c(APP(and, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))
   ENCODE_APP(or, cons_app(x1, x2)) -> c(APP(or, app(encArg(x1), encArg(x2))))
   ENCODE_APP(forall, cons_app(x1, x2)) -> c(APP(forall, 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(forsome, cons_app(x1, x2)) -> c(APP(forsome, 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))))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   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), forsome) -> c(APP(app(encArg(z0), encArg(z1)), forsome))
   ENCODE_APP(x0, cons_app(x1, and)) -> c(APP(encArg(x0), app(encArg(x1), and)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, or)) -> c(APP(encArg(x0), app(encArg(x1), or)))
   ENCODE_APP(x0, cons_app(x1, forall)) -> c(APP(encArg(x0), app(encArg(x1), forall)))
   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, forsome)) -> c(APP(encArg(x0), app(encArg(x1), forsome)))
   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(and, x2)) -> c(APP(encArg(x0), app(and, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(or, x2)) -> c(APP(encArg(x0), app(or, encArg(x2))))
   ENCODE_APP(x0, cons_app(forall, x2)) -> c(APP(encArg(x0), app(forall, 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(forsome, x2)) -> c(APP(encArg(x0), app(forsome, 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(and, cons_app(x1, x2)) -> c(APP(and, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))
   ENCODE_APP(or, cons_app(x1, x2)) -> c(APP(or, app(encArg(x1), encArg(x2))))
   ENCODE_APP(forall, cons_app(x1, x2)) -> c(APP(forall, 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(forsome, cons_app(x1, x2)) -> c(APP(forsome, 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(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1


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

(185) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ENCODE_APP(forall, cons_app(x1, x2)) -> c(APP(forall, app(encArg(x1), encArg(x2))))
   ENCODE_APP(forsome, cons_app(x1, x2)) -> c(APP(forsome, app(encArg(x1), encArg(x2))))
   ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2))))
   ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2))))
   ENCODE_APP(or, cons_app(x1, x2)) -> c(APP(or, app(encArg(x1), encArg(x2))))
   ENCODE_APP(and, cons_app(x1, x2)) -> c(APP(and, app(encArg(x1), encArg(x2))))
   ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2))))
   ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2))))

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(and) -> and
   encArg(true) -> true
   encArg(false) -> false
   encArg(or) -> or
   encArg(forall) -> forall
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(forsome) -> forsome
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(and, true), true) -> true
   app(app(and, z0), false) -> false
   app(app(and, false), z0) -> false
   app(app(or, true), z0) -> true
   app(app(or, z0), true) -> true
   app(app(or, false), false) -> false
   app(app(forall, z0), nil) -> true
   app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2))
   app(app(forsome, z0), nil) -> false
   app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2))
Tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1))
   ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1))
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(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))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(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(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(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), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
   ENCODE_APP(cons_app(z0, z1), and) -> c(APP(app(encArg(z0), encArg(z1)), and))
   ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true))
   ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false))
   ENCODE_APP(cons_app(z0, z1), or) -> c(APP(app(encArg(z0), encArg(z1)), or))
   ENCODE_APP(cons_app(z0, z1), forall) -> c(APP(app(encArg(z0), encArg(z1)), forall))
   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), forsome) -> c(APP(app(encArg(z0), encArg(z1)), forsome))
   ENCODE_APP(x0, cons_app(x1, and)) -> c(APP(encArg(x0), app(encArg(x1), and)))
   ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true)))
   ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false)))
   ENCODE_APP(x0, cons_app(x1, or)) -> c(APP(encArg(x0), app(encArg(x1), or)))
   ENCODE_APP(x0, cons_app(x1, forall)) -> c(APP(encArg(x0), app(encArg(x1), forall)))
   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, forsome)) -> c(APP(encArg(x0), app(encArg(x1), forsome)))
   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(and, x2)) -> c(APP(encArg(x0), app(and, encArg(x2))))
   ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2))))
   ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2))))
   ENCODE_APP(x0, cons_app(or, x2)) -> c(APP(encArg(x0), app(or, encArg(x2))))
   ENCODE_APP(x0, cons_app(forall, x2)) -> c(APP(encArg(x0), app(forall, 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(forsome, x2)) -> c(APP(encArg(x0), app(forsome, encArg(x2))))
   ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))))
S tuples:
   APP(app(and, true), true) -> c18
   APP(app(and, z0), false) -> c19
   APP(app(and, false), z0) -> c20
   APP(app(or, true), z0) -> c21
   APP(app(or, z0), true) -> c22
   APP(app(or, false), false) -> c23
   APP(app(forall, z0), nil) -> c24
   APP(app(forsome, z0), nil) -> c26
   APP(app(forall, app(and, z0)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, z0)), x2)), APP(app(and, z0), false), APP(app(forall, app(and, z0)), x2))
   APP(app(forall, app(and, false)), app(app(cons, z0), x2)) -> c25(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), z0), APP(app(forall, app(and, false)), x2))
   APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c25(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c25(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2))
   APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2))
   APP(app(forsome, app(or, true)), app(app(cons, z0), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), z0), APP(app(forsome, app(or, true)), x2))
   APP(app(forsome, app(or, z0)), app(app(cons, true), x2)) -> c27(APP(app(or, true), app(app(forsome, app(or, z0)), x2)), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), x2))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, x0), app(app(cons, x1), nil)) -> c25(APP(app(forall, x0), nil))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(and, z0), false))
   APP(app(forall, app(and, z0)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, z0)), nil))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(and, false), z0))
   APP(app(forall, app(and, false)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(and, false)), nil))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(or, true), z0))
   APP(app(forall, app(or, true)), app(app(cons, z0), nil)) -> c1(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(or, z0), true))
   APP(app(forall, app(or, z0)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, z0)), nil))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false))
   APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil)))
   APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c25(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(and, z0), x1)), app(app(and, false), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forall, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c25(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c25(APP(app(and, app(app(or, z0), x1)), app(app(and, true), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forall, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c25(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c25(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, z0), x2)), app(app(forall, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forall, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forall, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forall, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(or, z0), x2)), app(app(forall, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forall, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c25(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c25(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c25(APP(app(and, true), true), APP(app(forall, app(and, true)), x0))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true))
   APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil))
   APP(app(forall, app(or, true)), app(app(cons, x0), x1)) -> c25(APP(app(or, true), x0), APP(app(forall, app(or, true)), x1))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(and, true), true))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(or, true), x0))
   APP(app(forall, app(or, true)), app(app(cons, x0), nil)) -> c3(APP(app(forall, app(or, true)), nil))
   APP(app(forall, app(or, x0)), app(app(cons, true), x1)) -> c25(APP(app(or, x0), true), APP(app(forall, app(or, x0)), x1))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(and, true), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(or, x0), true))
   APP(app(forall, app(or, x0)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(or, x0)), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c25(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(and, true), true))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, x0), nil))
   APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c5(APP(app(forall, app(forall, x0)), nil))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3))
   APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3))
   APP(app(forall, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forall, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, z0))), x3))
   APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(and, false))), x3))
   APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forall, app(or, true))), x3))
   APP(app(forall, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forall, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, z0))), x3))
   APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3))
   APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forall, x0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c25(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3))
   APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(or, true))), x3))
   APP(app(forall, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forall, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, z0))), x3))
   APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3))
   APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3))
   APP(app(forall, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forall, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, z0))), x3))
   APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forall, app(forsome, app(and, false))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c25(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c25(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3))
   APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c25(APP(app(forall, app(forsome, x0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, x0), app(app(cons, x1), nil)) -> c27(APP(app(forsome, x0), nil))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true))
   APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(and, true)), nil))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(and, z0), false))
   APP(app(forsome, app(and, z0)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(and, z0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(and, false), z0))
   APP(app(forsome, app(and, false)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(or, true), z0))
   APP(app(forsome, app(or, true)), app(app(cons, z0), nil)) -> c6(APP(app(forsome, app(or, true)), nil))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(or, z0), true))
   APP(app(forsome, app(or, z0)), app(app(cons, true), nil)) -> c6(APP(app(forsome, app(or, z0)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c6(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, true), false))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forall, z0), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forall, z0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(or, false), false))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, z0), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c6(APP(app(forsome, app(forsome, z0)), nil))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil)))
   APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2))))
   APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(and, z0), x1)), app(app(or, false), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), x1), APP(app(forsome, app(and, z0)), app(app(cons, false), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, z0), x3))) -> c27(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, z0), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(or, app(app(or, z0), x1)), app(app(or, true), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), x1), APP(app(forsome, app(or, z0)), app(app(cons, true), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))
   APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, z0)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, z0), x2)), app(app(forsome, app(and, z0)), x3))), APP(app(and, z0), false), APP(app(forsome, app(and, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, false)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), z0), APP(app(forsome, app(and, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, true)), app(app(cons, z0), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), z0), APP(app(forsome, app(or, true)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, z0)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(or, z0), x2)), app(app(forsome, app(or, z0)), x3))), APP(app(or, z0), true), APP(app(forsome, app(or, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3)))
   APP(app(forsome, app(and, x0)), app(app(cons, false), x1)) -> c27(APP(app(and, x0), false), APP(app(forsome, app(and, x0)), x1))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(or, false), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(and, x0), false))
   APP(app(forsome, app(and, x0)), app(app(cons, false), nil)) -> c7(APP(app(forsome, app(and, x0)), nil))
   APP(app(forsome, app(and, false)), app(app(cons, x0), x1)) -> c27(APP(app(and, false), x0), APP(app(forsome, app(and, false)), x1))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(or, false), false))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(and, false), x0))
   APP(app(forsome, app(and, false)), app(app(cons, x0), nil)) -> c9(APP(app(forsome, app(and, false)), nil))
   APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false))
   APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forsome, app(or, false)), nil))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3))
   APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3))
   APP(app(forsome, app(forall, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, z0)), x2))), app(app(forsome, app(forall, app(and, z0))), x3)), APP(app(forall, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, z0))), x3))
   APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(and, false))), x3))
   APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forall, app(or, true))), x3))
   APP(app(forsome, app(forall, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(or, z0)), x2))), app(app(forsome, app(forall, app(or, z0))), x3)), APP(app(forall, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, z0))), x3))
   APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3))
   APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forall, x0)), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(or, false), false))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, x0), nil))
   APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forsome, app(forsome, x0)), nil))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3))
   APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(or, true))), x3))
   APP(app(forsome, app(forsome, app(or, z0))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(or, z0)), x2))), app(app(forsome, app(forsome, app(or, z0))), x3)), APP(app(forsome, app(or, z0)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, z0))), x3))
   APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3))
   APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3))
   APP(app(forsome, app(forsome, app(and, z0))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, z0)), x2))), app(app(forsome, app(forsome, app(and, z0))), x3)), APP(app(forsome, app(and, z0)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, z0))), x3))
   APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, z0), x2)), APP(app(forsome, app(forsome, app(and, false))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3))
   APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forsome, app(forsome, x0)), x3))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c18, c19, c20, c21, c22, c23, c24, c26, c8_1, c25_3, c27_3, c_1, c8_3, c8_2, c25_1, c1_1, c25_2, c2_1, c3_1, c4_1, c5_1, c27_1, c6_1, c27_2, c7_1, c9_1, c10_1, c11_1