KILLED
proof of input_Td8le5XExs.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (14) CpxRNTS
        (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (16) CpxRNTS
    (17) CompletionProof [UPPER BOUND(ID), 0 ms]
    (18) CpxTypedWeightedCompleteTrs
        (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (20) CpxRNTS
(21) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(22) CdtProblem
    (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CdtProblem
    (25) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CdtProblem
    (27) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) CdtProblem
    (29) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CdtProblem
    (33) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms]
    (62) CdtProblem
    (63) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 168 ms]
    (80) CdtProblem
    (81) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 115 ms]
    (88) CdtProblem
    (89) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 127 ms]
    (90) CdtProblem


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(x, nil) -> x
   foldf(x, cons(y, z)) -> f(foldf(x, z), y)
   f(t, x) -> f'(t, g(x))
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c))
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b))
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c)

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

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

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


The TRS R consists of the following rules:

   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(x, nil) -> x
   foldf(x, cons(y, z)) -> f(foldf(x, z), y)
   f(t, x) -> f'(t, g(x))
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c))
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b))
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c)

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

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

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


The TRS R consists of the following rules:

   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(x, nil) -> x
   foldf(x, cons(y, z)) -> f(foldf(x, z), y)
   f(t, x) -> f'(t, g(x))
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c))
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b))
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c)

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

(5) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(6)
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:

   g(A) -> A [1]
   g(B) -> A [1]
   g(B) -> B [1]
   g(C) -> A [1]
   g(C) -> B [1]
   g(C) -> C [1]
   foldf(x, nil) -> x [1]
   foldf(x, cons(y, z)) -> f(foldf(x, z), y) [1]
   f(t, x) -> f'(t, g(x)) [1]
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) [1]
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A) [1]
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b)) [1]
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) [1]

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

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

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   g(A) -> A [1]
   g(B) -> A [1]
   g(B) -> B [1]
   g(C) -> A [1]
   g(C) -> B [1]
   g(C) -> C [1]
   foldf(x, nil) -> x [1]
   foldf(x, cons(y, z)) -> f(foldf(x, z), y) [1]
   f(t, x) -> f'(t, g(x)) [1]
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) [1]
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A) [1]
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b)) [1]
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) [1]

The TRS has the following type information:
g :: A:B:C -> A:B:C
A :: A:B:C
B :: A:B:C
C :: A:B:C
foldf :: triple -> nil:cons -> triple
nil :: nil:cons
cons :: A:B:C -> nil:cons -> nil:cons
f :: triple -> A:B:C -> triple
f' :: triple -> A:B:C -> triple
triple :: nil:cons -> nil:cons -> nil:cons -> triple
f'' :: triple -> triple

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

(9) 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:

   g_1
   foldf_2
   f_2
   f'_2
   f''_1

Due to the following rules being added:

   f'(v0, v1) -> const [0]
   f''(v0) -> const [0]

And the following fresh constants:    const

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

(10)
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:

   g(A) -> A [1]
   g(B) -> A [1]
   g(B) -> B [1]
   g(C) -> A [1]
   g(C) -> B [1]
   g(C) -> C [1]
   foldf(x, nil) -> x [1]
   foldf(x, cons(y, z)) -> f(foldf(x, z), y) [1]
   f(t, x) -> f'(t, g(x)) [1]
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) [1]
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A) [1]
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b)) [1]
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) [1]
   f'(v0, v1) -> const [0]
   f''(v0) -> const [0]

The TRS has the following type information:
g :: A:B:C -> A:B:C
A :: A:B:C
B :: A:B:C
C :: A:B:C
foldf :: triple:const -> nil:cons -> triple:const
nil :: nil:cons
cons :: A:B:C -> nil:cons -> nil:cons
f :: triple:const -> A:B:C -> triple:const
f' :: triple:const -> A:B:C -> triple:const
triple :: nil:cons -> nil:cons -> nil:cons -> triple:const
f'' :: triple:const -> triple:const
const :: triple:const

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

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

(12)
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:

   g(A) -> A [1]
   g(B) -> A [1]
   g(B) -> B [1]
   g(C) -> A [1]
   g(C) -> B [1]
   g(C) -> C [1]
   foldf(x, nil) -> x [1]
   foldf(x, cons(y, nil)) -> f(x, y) [2]
   foldf(x, cons(y, cons(y', z'))) -> f(f(foldf(x, z'), y'), y) [2]
   f(t, A) -> f'(t, A) [2]
   f(t, B) -> f'(t, A) [2]
   f(t, B) -> f'(t, B) [2]
   f(t, C) -> f'(t, A) [2]
   f(t, C) -> f'(t, B) [2]
   f(t, C) -> f'(t, C) [2]
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) [1]
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A) [1]
   f'(triple(a, nil, c), A) -> f''(triple(cons(A, a), nil, c)) [2]
   f'(triple(a, cons(y'', z''), c), A) -> f''(f(foldf(triple(cons(A, a), nil, c), z''), y'')) [2]
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) [1]
   f'(v0, v1) -> const [0]
   f''(v0) -> const [0]

The TRS has the following type information:
g :: A:B:C -> A:B:C
A :: A:B:C
B :: A:B:C
C :: A:B:C
foldf :: triple:const -> nil:cons -> triple:const
nil :: nil:cons
cons :: A:B:C -> nil:cons -> nil:cons
f :: triple:const -> A:B:C -> triple:const
f' :: triple:const -> A:B:C -> triple:const
triple :: nil:cons -> nil:cons -> nil:cons -> triple:const
f'' :: triple:const -> triple:const
const :: triple:const

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

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

   A => 0
   B => 1
   C => 2
   nil => 0
   const => 0

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z, z1) -{ 2 }-> f'(t, 2) :|: z1 = 2, z = t, t >= 0
   f(z, z1) -{ 2 }-> f'(t, 1) :|: z = t, z1 = 1, t >= 0
   f(z, z1) -{ 2 }-> f'(t, 1) :|: z1 = 2, z = t, t >= 0
   f(z, z1) -{ 2 }-> f'(t, 0) :|: z1 = 0, z = t, t >= 0
   f(z, z1) -{ 2 }-> f'(t, 0) :|: z = t, z1 = 1, t >= 0
   f(z, z1) -{ 2 }-> f'(t, 0) :|: z1 = 2, z = t, t >= 0
   f'(z, z1) -{ 2 }-> f''(f(foldf(1 + (1 + 0 + a) + 0 + c, z''), y'')) :|: z1 = 0, a >= 0, c >= 0, z'' >= 0, z = 1 + a + (1 + y'' + z'') + c, y'' >= 0
   f'(z, z1) -{ 2 }-> f''(1 + (1 + 0 + a) + 0 + c) :|: z1 = 0, a >= 0, c >= 0, z = 1 + a + 0 + c
   f'(z, z1) -{ 1 }-> f(1 + a + b + c, 0) :|: b >= 0, a >= 0, c >= 0, z1 = 1, z = 1 + a + b + c
   f'(z, z1) -{ 0 }-> 0 :|: v0 >= 0, z1 = v1, v1 >= 0, z = v0
   f'(z, z1) -{ 1 }-> 1 + a + b + (1 + 2 + c) :|: b >= 0, z1 = 2, a >= 0, c >= 0, z = 1 + a + b + c
   f''(z) -{ 1 }-> foldf(1 + a + b + 0, c) :|: b >= 0, a >= 0, c >= 0, z = 1 + a + b + c
   f''(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   foldf(z, z1) -{ 1 }-> x :|: z1 = 0, x >= 0, z = x
   foldf(z, z1) -{ 2 }-> f(x, y) :|: x >= 0, y >= 0, z = x, z1 = 1 + y + 0
   foldf(z, z1) -{ 2 }-> f(f(foldf(x, z'), y'), y) :|: z1 = 1 + y + (1 + y' + z'), x >= 0, y >= 0, z' >= 0, y' >= 0, z = x
   g(z) -{ 1 }-> 2 :|: z = 2
   g(z) -{ 1 }-> 1 :|: z = 1
   g(z) -{ 1 }-> 1 :|: z = 2
   g(z) -{ 1 }-> 0 :|: z = 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 0 :|: z = 2


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

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

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z, z1) -{ 2 }-> f'(z, 2) :|: z1 = 2, z >= 0
   f(z, z1) -{ 2 }-> f'(z, 1) :|: z1 = 1, z >= 0
   f(z, z1) -{ 2 }-> f'(z, 1) :|: z1 = 2, z >= 0
   f(z, z1) -{ 2 }-> f'(z, 0) :|: z1 = 0, z >= 0
   f(z, z1) -{ 2 }-> f'(z, 0) :|: z1 = 1, z >= 0
   f(z, z1) -{ 2 }-> f'(z, 0) :|: z1 = 2, z >= 0
   f'(z, z1) -{ 2 }-> f''(f(foldf(1 + (1 + 0 + a) + 0 + c, z''), y'')) :|: z1 = 0, a >= 0, c >= 0, z'' >= 0, z = 1 + a + (1 + y'' + z'') + c, y'' >= 0
   f'(z, z1) -{ 2 }-> f''(1 + (1 + 0 + a) + 0 + c) :|: z1 = 0, a >= 0, c >= 0, z = 1 + a + 0 + c
   f'(z, z1) -{ 1 }-> f(1 + a + b + c, 0) :|: b >= 0, a >= 0, c >= 0, z1 = 1, z = 1 + a + b + c
   f'(z, z1) -{ 0 }-> 0 :|: z >= 0, z1 >= 0
   f'(z, z1) -{ 1 }-> 1 + a + b + (1 + 2 + c) :|: b >= 0, z1 = 2, a >= 0, c >= 0, z = 1 + a + b + c
   f''(z) -{ 1 }-> foldf(1 + a + b + 0, c) :|: b >= 0, a >= 0, c >= 0, z = 1 + a + b + c
   f''(z) -{ 0 }-> 0 :|: z >= 0
   foldf(z, z1) -{ 1 }-> z :|: z1 = 0, z >= 0
   foldf(z, z1) -{ 2 }-> f(z, z1 - 1) :|: z >= 0, z1 - 1 >= 0
   foldf(z, z1) -{ 2 }-> f(f(foldf(z, z'), y'), y) :|: z1 = 1 + y + (1 + y' + z'), z >= 0, y >= 0, z' >= 0, y' >= 0
   g(z) -{ 1 }-> 2 :|: z = 2
   g(z) -{ 1 }-> 1 :|: z = 1
   g(z) -{ 1 }-> 1 :|: z = 2
   g(z) -{ 1 }-> 0 :|: z = 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 0 :|: z = 2


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

(17) 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:

   f'(v0, v1) -> null_f' [0]
   f''(v0) -> null_f'' [0]

And the following fresh constants:    null_f', null_f''

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

(18)
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:

   g(A) -> A [1]
   g(B) -> A [1]
   g(B) -> B [1]
   g(C) -> A [1]
   g(C) -> B [1]
   g(C) -> C [1]
   foldf(x, nil) -> x [1]
   foldf(x, cons(y, z)) -> f(foldf(x, z), y) [1]
   f(t, x) -> f'(t, g(x)) [1]
   f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) [1]
   f'(triple(a, b, c), B) -> f(triple(a, b, c), A) [1]
   f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b)) [1]
   f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) [1]
   f'(v0, v1) -> null_f' [0]
   f''(v0) -> null_f'' [0]

The TRS has the following type information:
g :: A:B:C -> A:B:C
A :: A:B:C
B :: A:B:C
C :: A:B:C
foldf :: triple:null_f':null_f'' -> nil:cons -> triple:null_f':null_f''
nil :: nil:cons
cons :: A:B:C -> nil:cons -> nil:cons
f :: triple:null_f':null_f'' -> A:B:C -> triple:null_f':null_f''
f' :: triple:null_f':null_f'' -> A:B:C -> triple:null_f':null_f''
triple :: nil:cons -> nil:cons -> nil:cons -> triple:null_f':null_f''
f'' :: triple:null_f':null_f'' -> triple:null_f':null_f''
null_f' :: triple:null_f':null_f''
null_f'' :: triple:null_f':null_f''

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

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

   A => 0
   B => 1
   C => 2
   nil => 0
   null_f' => 0
   null_f'' => 0

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

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z', z'') -{ 1 }-> f'(t, g(x)) :|: z' = t, x >= 0, z'' = x, t >= 0
   f'(z', z'') -{ 1 }-> f''(foldf(1 + (1 + 0 + a) + 0 + c, b)) :|: z'' = 0, b >= 0, a >= 0, c >= 0, z' = 1 + a + b + c
   f'(z', z'') -{ 1 }-> f(1 + a + b + c, 0) :|: b >= 0, a >= 0, c >= 0, z' = 1 + a + b + c, z'' = 1
   f'(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   f'(z', z'') -{ 1 }-> 1 + a + b + (1 + 2 + c) :|: b >= 0, a >= 0, c >= 0, z'' = 2, z' = 1 + a + b + c
   f''(z') -{ 1 }-> foldf(1 + a + b + 0, c) :|: b >= 0, a >= 0, c >= 0, z' = 1 + a + b + c
   f''(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   foldf(z', z'') -{ 1 }-> x :|: z'' = 0, z' = x, x >= 0
   foldf(z', z'') -{ 1 }-> f(foldf(x, z), y) :|: z >= 0, z' = x, x >= 0, y >= 0, z'' = 1 + y + z
   g(z') -{ 1 }-> 2 :|: z' = 2
   g(z') -{ 1 }-> 1 :|: z' = 1
   g(z') -{ 1 }-> 1 :|: z' = 2
   g(z') -{ 1 }-> 0 :|: z' = 0
   g(z') -{ 1 }-> 0 :|: z' = 1
   g(z') -{ 1 }-> 0 :|: z' = 2

Only complete derivations are relevant for the runtime complexity.

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

(21) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(22)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   G(A) -> c
   G(B) -> c1
   G(B) -> c2
   G(C) -> c3
   G(C) -> c4
   G(C) -> c5
   FOLDF(z0, nil) -> c6
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(z0, z1) -> c8(F'(z0, g(z1)), G(z1))
   F'(triple(z0, z1, z2), C) -> c9
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
S tuples:
   G(A) -> c
   G(B) -> c1
   G(B) -> c2
   G(C) -> c3
   G(C) -> c4
   G(C) -> c5
   FOLDF(z0, nil) -> c6
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(z0, z1) -> c8(F'(z0, g(z1)), G(z1))
   F'(triple(z0, z1, z2), C) -> c9
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   G_1, FOLDF_2, F_2, F'_2, F''_1

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7_2, c8_2, c9, c10_1, c11_2, c12_1


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

(23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   G(C) -> c4
   F'(triple(z0, z1, z2), C) -> c9
   FOLDF(z0, nil) -> c6
   G(B) -> c2
   G(C) -> c3
   G(B) -> c1
   G(A) -> c
   G(C) -> c5

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

(24)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(z0, z1) -> c8(F'(z0, g(z1)), G(z1))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(z0, z1) -> c8(F'(z0, g(z1)), G(z1))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F_2, F'_2, F''_1

Compound Symbols:   c7_2, c8_2, c10_1, c11_2, c12_1


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

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F(z0, z1) -> c8(F'(z0, g(z1)))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F(z0, z1) -> c8(F'(z0, g(z1)))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c10_1, c11_2, c12_1, c8_1


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

(27) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F'(triple(z0, z1, z2), A) -> c11(F''(foldf(triple(cons(A, z0), nil, z2), z1)), FOLDF(triple(cons(A, z0), nil, z2), z1)) by 
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)), FOLDF(triple(cons(A, x0), nil, x2), nil))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))

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

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F(z0, z1) -> c8(F'(z0, g(z1)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)), FOLDF(triple(cons(A, x0), nil, x2), nil))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F(z0, z1) -> c8(F'(z0, g(z1)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)), FOLDF(triple(cons(A, x0), nil, x2), nil))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c10_1, c12_1, c8_1, c11_2


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

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

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F(z0, z1) -> c8(F'(z0, g(z1)))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F(z0, z1) -> c8(F'(z0, g(z1)))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c10_1, c12_1, c8_1, c11_2, c11_1


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

(31) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(z0, z1) -> c8(F'(z0, g(z1))) by 
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, C))

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, C))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, C))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c10_1, c12_1, c11_2, c11_1, c8_1


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

(33) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   F(x0, C) -> c8(F'(x0, C))

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2)))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c10_1, c12_1, c11_2, c11_1, c8_1


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

(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F'(triple(x0, cons(z1, z2), x2), A) -> c11(F''(f(foldf(triple(cons(A, x0), nil, x2), z2), z1)), FOLDF(triple(cons(A, x0), nil, x2), cons(z1, z2))) by 
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c10_1, c12_1, c11_1, c8_1, c11_2


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

(37) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F''(triple(z0, z1, z2)) -> c12(FOLDF(triple(z0, z1, nil), z2)) by 
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2)))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F_2, F''_1

Compound Symbols:   c7_2, c10_1, c11_1, c8_1, c11_2, c12_1


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

(39) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F'(triple(x0, nil, x2), A) -> c11(F''(triple(cons(A, x0), nil, x2))) by 
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F(x0, A) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F_2, F''_1

Compound Symbols:   c7_2, c10_1, c8_1, c11_2, c11_1, c12_1


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

(41) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(x0, A) -> c8(F'(x0, A)) by 
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F_2, F''_1

Compound Symbols:   c7_2, c10_1, c8_1, c11_2, c11_1, c12_1


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

(43) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F'(triple(z0, z1, z2), B) -> c10(F(triple(z0, z1, z2), A)) by 
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, B) -> c8(F'(x0, A))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F_2, F'_2, F''_1

Compound Symbols:   c7_2, c8_1, c11_2, c11_1, c12_1, c10_1


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

(45) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(x0, B) -> c8(F'(x0, A)) by 
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, B) -> c8(F'(x0, B))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F_2, F'_2, F''_1

Compound Symbols:   c7_2, c8_1, c11_2, c11_1, c12_1, c10_1


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

(47) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(x0, B) -> c8(F'(x0, B)) by 
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, C) -> c8(F'(x0, A))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F_2, F'_2, F''_1

Compound Symbols:   c7_2, c8_1, c11_2, c11_1, c12_1, c10_1


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

(49) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(x0, C) -> c8(F'(x0, A)) by 
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F(x0, C) -> c8(F'(x0, B))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F_2, F'_2, F''_1

Compound Symbols:   c7_2, c8_1, c11_2, c11_1, c12_1, c10_1


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

(51) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(x0, C) -> c8(F'(x0, B)) by 
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
S tuples:
   FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2))
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   FOLDF_2, F'_2, F''_1, F_2

Compound Symbols:   c7_2, c11_2, c11_1, c12_1, c8_1, c10_1


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace FOLDF(z0, cons(z1, z2)) -> c7(F(foldf(z0, z2), z1), FOLDF(z0, z2)) by 
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1), FOLDF(z0, nil))
   FOLDF(z0, cons(x1, cons(z1, z2))) -> c7(F(f(foldf(z0, z2), z1), x1), FOLDF(z0, cons(z1, z2)))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1), FOLDF(z0, nil))
   FOLDF(z0, cons(x1, cons(z1, z2))) -> c7(F(f(foldf(z0, z2), z1), x1), FOLDF(z0, cons(z1, z2)))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1), FOLDF(z0, nil))
   FOLDF(z0, cons(x1, cons(z1, z2))) -> c7(F(f(foldf(z0, z2), z1), x1), FOLDF(z0, cons(z1, z2)))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F''_1, F_2, FOLDF_2

Compound Symbols:   c11_2, c11_1, c12_1, c8_1, c10_1, c7_2


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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, cons(z1, z2))) -> c7(F(f(foldf(z0, z2), z1), x1), FOLDF(z0, cons(z1, z2)))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, cons(z1, z2))) -> c7(F(f(foldf(z0, z2), z1), x1), FOLDF(z0, cons(z1, z2)))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F''_1, F_2, FOLDF_2

Compound Symbols:   c11_2, c11_1, c12_1, c8_1, c10_1, c7_2, c7_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace FOLDF(z0, cons(x1, cons(z1, z2))) -> c7(F(f(foldf(z0, z2), z1), x1), FOLDF(z0, cons(z1, z2))) by 
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2)))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F''_1, F_2, FOLDF_2

Compound Symbols:   c11_2, c11_1, c12_1, c8_1, c10_1, c7_1, c7_2


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

(59) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F'(triple(x0, cons(x1, x2), x3), A) -> c11(FOLDF(triple(cons(A, x0), nil, x3), cons(x1, x2))) by 
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2)))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F''_1, F_2, FOLDF_2

Compound Symbols:   c11_2, c12_1, c11_1, c8_1, c10_1, c7_1, c7_2


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

(61) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F''(triple(z0, z1, cons(y1, y2))) -> c12(FOLDF(triple(z0, z1, nil), cons(y1, y2))) by 
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c11_1, c8_1, c10_1, c7_1, c7_2, c12_1


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

(63) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F'(triple(z0, nil, cons(y2, y3)), A) -> c11(F''(triple(cons(A, z0), nil, cons(y2, y3)))) by 
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(65) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(triple(y0, nil, cons(y1, y2)), A) -> c8(F'(triple(y0, nil, cons(y1, y2)), A)) by 
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(67) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F'(triple(z0, nil, cons(y1, y2)), B) -> c10(F(triple(z0, nil, cons(y1, y2)), A)) by 
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(69) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), A)) by 
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(71) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(triple(y0, nil, cons(y1, y2)), B) -> c8(F'(triple(y0, nil, cons(y1, y2)), B)) by 
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(73) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), A)) by 
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(75) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(triple(y0, nil, cons(y1, y2)), C) -> c8(F'(triple(y0, nil, cons(y1, y2)), B)) by 
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_1, c7_2, c11_1, c12_1


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

(77) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace FOLDF(z0, cons(x1, nil)) -> c7(F(z0, x1)) by 
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
K tuples:none
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1


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

(79) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
We considered the (Usable) Rules:
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f(z0, z1) -> f'(z0, g(z1))
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
And the Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(A) = 0
   POL(B) = 0
   POL(C) = 0
   POL(F(x_1, x_2)) = 0
   POL(F'(x_1, x_2)) = x_2
   POL(F''(x_1)) = x_1
   POL(FOLDF(x_1, x_2)) = x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1]
   POL(f(x_1, x_2)) = x_1
   POL(f'(x_1, x_2)) = x_1
   POL(f''(x_1)) = x_1
   POL(foldf(x_1, x_2)) = x_1
   POL(g(x_1)) = [1] + x_1
   POL(nil) = 0
   POL(triple(x_1, x_2, x_3)) = x_2

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil)))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
K tuples:
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1


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

(81) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F'(triple(z0, cons(z1, nil), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, nil))) by 
   F'(triple(z0, cons(A, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil)))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
K tuples:
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1


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

(83) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F''(triple(z0, z1, cons(z2, nil))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, nil))) by 
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
K tuples:
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1


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

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 13 trailing nodes:
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), A))
   F'(triple(z0, cons(C, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(C, nil)))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), C))
   F'(triple(z0, cons(A, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(A, nil)))
   F(triple(z0, nil, cons(z1, nil)), B) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), B))
   F'(triple(z0, nil, cons(z1, nil)), B) -> c10(F(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, nil)), C) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   F(triple(z0, nil, cons(z1, nil)), A) -> c8(F'(triple(z0, nil, cons(z1, nil)), A))
   FOLDF(triple(y0, nil, cons(y1, nil)), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, nil)), B))
   F'(triple(z0, cons(B, nil), cons(y1, nil)), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, nil)), cons(B, nil)))
   F'(triple(z0, nil, cons(z1, nil)), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, nil))))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
K tuples:
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1


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

(87) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
We considered the (Usable) Rules:
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f(z0, z1) -> f'(z0, g(z1))
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
And the Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(A) = [1]
   POL(B) = 0
   POL(C) = 0
   POL(F(x_1, x_2)) = x_1
   POL(F'(x_1, x_2)) = x_1
   POL(F''(x_1)) = x_1
   POL(FOLDF(x_1, x_2)) = x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = x_1
   POL(f(x_1, x_2)) = 0
   POL(f'(x_1, x_2)) = 0
   POL(f''(x_1)) = 0
   POL(foldf(x_1, x_2)) = x_1
   POL(g(x_1)) = [1] + x_1
   POL(nil) = 0
   POL(triple(x_1, x_2, x_3)) = x_3

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
K tuples:
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1


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

(89) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
We considered the (Usable) Rules:
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f(z0, z1) -> f'(z0, g(z1))
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
And the Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(A) = 0
   POL(B) = 0
   POL(C) = 0
   POL(F(x_1, x_2)) = 0
   POL(F'(x_1, x_2)) = x_2
   POL(F''(x_1)) = x_1
   POL(FOLDF(x_1, x_2)) = 0
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1]
   POL(f(x_1, x_2)) = x_1
   POL(f'(x_1, x_2)) = x_1
   POL(f''(x_1)) = x_1
   POL(foldf(x_1, x_2)) = x_1
   POL(g(x_1)) = [1] + x_1
   POL(nil) = 0
   POL(triple(x_1, x_2, x_3)) = x_2

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(A) -> A
   g(B) -> A
   g(B) -> B
   g(C) -> A
   g(C) -> B
   g(C) -> C
   foldf(z0, nil) -> z0
   foldf(z0, cons(z1, z2)) -> f(foldf(z0, z2), z1)
   f(z0, z1) -> f'(z0, g(z1))
   f'(triple(z0, z1, z2), C) -> triple(z0, z1, cons(C, z2))
   f'(triple(z0, z1, z2), B) -> f(triple(z0, z1, z2), A)
   f'(triple(z0, z1, z2), A) -> f''(foldf(triple(cons(A, z0), nil, z2), z1))
   f''(triple(z0, z1, z2)) -> foldf(triple(z0, z1, nil), z2)
Tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
S tuples:
   F'(triple(x0, cons(z1, x2), x3), A) -> c11(F''(f'(foldf(triple(cons(A, x0), nil, x3), x2), g(z1))), FOLDF(triple(cons(A, x0), nil, x3), cons(z1, x2)))
   F'(triple(x0, cons(x1, nil), x3), A) -> c11(F''(f(triple(cons(A, x0), nil, x3), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, nil)))
   F'(triple(x0, cons(x1, cons(z1, z2)), x3), A) -> c11(F''(f(f(foldf(triple(cons(A, x0), nil, x3), z2), z1), x1)), FOLDF(triple(cons(A, x0), nil, x3), cons(x1, cons(z1, z2))))
   F(triple(y0, cons(y1, y2), y3), A) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), A) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), A) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F'(triple(z0, cons(y1, y2), z2), B) -> c10(F(triple(z0, cons(y1, y2), z2), A))
   F'(triple(z0, cons(y1, nil), z2), B) -> c10(F(triple(z0, cons(y1, nil), z2), A))
   F'(triple(z0, cons(y1, cons(y2, y3)), z2), B) -> c10(F(triple(z0, cons(y1, cons(y2, y3)), z2), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), B) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), B) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), B) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), A))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), A))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   F(triple(y0, cons(y1, y2), y3), C) -> c8(F'(triple(y0, cons(y1, y2), y3), B))
   F(triple(y0, cons(y1, nil), y2), C) -> c8(F'(triple(y0, cons(y1, nil), y2), B))
   F(triple(y0, cons(y1, cons(y2, y3)), y4), C) -> c8(F'(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(x0, cons(x1, cons(z1, x3))) -> c7(F(f'(foldf(x0, x3), g(z1)), x1), FOLDF(x0, cons(z1, x3)))
   FOLDF(z0, cons(x1, cons(x2, nil))) -> c7(F(f(z0, x2), x1), FOLDF(z0, cons(x2, nil)))
   FOLDF(z0, cons(x1, cons(x2, cons(z1, z2)))) -> c7(F(f(f(foldf(z0, z2), z1), x2), x1), FOLDF(z0, cons(x2, cons(z1, z2))))
   F'(triple(z0, cons(z1, cons(y2, y3)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, y3))))
   F'(triple(z0, cons(z1, cons(y2, nil)), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, nil))))
   F'(triple(z0, cons(z1, cons(y2, cons(y3, y4))), z3), A) -> c11(FOLDF(triple(cons(A, z0), nil, z3), cons(z1, cons(y2, cons(y3, y4)))))
   F''(triple(z0, z1, cons(z2, cons(y2, y3)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, y3))))
   F''(triple(z0, z1, cons(z2, cons(y2, nil)))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, nil))))
   F''(triple(z0, z1, cons(z2, cons(y2, cons(y3, y4))))) -> c12(FOLDF(triple(z0, z1, nil), cons(z2, cons(y2, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, y4))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, y4)))))
   F'(triple(z0, nil, cons(z1, cons(y3, nil))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, nil)))))
   F'(triple(z0, nil, cons(z1, cons(y3, cons(y4, y5)))), A) -> c11(F''(triple(cons(A, z0), nil, cons(z1, cons(y3, cons(y4, y5))))))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c10(F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), A))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), A))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), A))
   F(triple(z0, nil, cons(z1, cons(y2, y3))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, y3))), B))
   F(triple(z0, nil, cons(z1, cons(y2, nil))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, nil))), B))
   F(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), C) -> c8(F'(triple(z0, nil, cons(z1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), A))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), B))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, y3))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, y3))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, nil))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, nil))), C))
   FOLDF(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)) -> c7(F(triple(y0, nil, cons(y1, cons(y2, cons(y3, y4)))), C))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(A, nil)))
   F'(triple(z0, cons(A, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(A, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(B, nil)))
   F'(triple(z0, cons(B, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(B, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, y3))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, y3))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, nil))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, nil))), cons(C, nil)))
   F'(triple(z0, cons(C, nil), cons(y1, cons(y2, cons(y3, y4)))), A) -> c11(FOLDF(triple(cons(A, z0), nil, cons(y1, cons(y2, cons(y3, y4)))), cons(C, nil)))
K tuples:
   FOLDF(triple(y0, cons(y1, y2), y3), cons(A, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), A))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(A, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), A))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(A, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), A))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(B, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), B))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(B, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), B))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(B, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), B))
   FOLDF(triple(y0, cons(y1, y2), y3), cons(C, nil)) -> c7(F(triple(y0, cons(y1, y2), y3), C))
   FOLDF(triple(y0, cons(y1, nil), y2), cons(C, nil)) -> c7(F(triple(y0, cons(y1, nil), y2), C))
   FOLDF(triple(y0, cons(y1, cons(y2, y3)), y4), cons(C, nil)) -> c7(F(triple(y0, cons(y1, cons(y2, y3)), y4), C))
   F''(triple(z0, cons(y1, y2), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, nil), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(A, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(A, nil)))
   F''(triple(z0, cons(y1, y2), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, nil), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(B, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(B, nil)))
   F''(triple(z0, cons(y1, y2), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, y2), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, nil), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, nil), nil), cons(C, nil)))
   F''(triple(z0, cons(y1, cons(y2, y3)), cons(C, nil))) -> c12(FOLDF(triple(z0, cons(y1, cons(y2, y3)), nil), cons(C, nil)))
Defined Rule Symbols:   g_1, foldf_2, f_2, f'_2, f''_1

Defined Pair Symbols:   F'_2, F_2, FOLDF_2, F''_1

Compound Symbols:   c11_2, c8_1, c10_1, c7_2, c11_1, c12_1, c7_1